ko

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

인기 있는 삼각법 >

tan(x+pi/4)-tan(x-pi/4)=3

해법

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

해법

x = - 0.42053 \dots + πn, x = 0.42053 \dots + πn

+1

도

x = - 24.09484 \dots^{\circ} + 18 0^{\circ} n, x = 24.09484 \dots^{\circ} + 18 0^{\circ} n

솔루션 단계

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

삼각성을 사용하여 다시 쓰기

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

삼각성을 사용하여 다시 쓰기

tan (x - \frac{π}{4})

기본 삼각형 항등식 사용:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x - \frac{π}{4} )}{cos ( x - \frac{π}{4} )}

각도 차이 식별 사용:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= \frac{sin ( x ) cos ( \frac{π}{4} ) - cos ( x ) sin ( \frac{π}{4} )}{cos ( x - \frac{π}{4} )}

각도 차이 식별 사용:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= \frac{sin ( x ) cos ( \frac{π}{4} ) - cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) + sin ( x ) sin ( \frac{π}{4} )}

\frac{sin ( x ) cos ( \frac{π}{4} ) - cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) + sin ( x ) sin ( \frac{π}{4} )}

단순화하세요:

\frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )}

\frac{sin ( x ) cos ( \frac{π}{4} ) - cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) + sin ( x ) sin ( \frac{π}{4} )}

sin (x) cos (\frac{π}{4}) - cos (x) sin (\frac{π}{4}) = \frac{2}{2} sin (x) - \frac{2}{2} cos (x)

sin (x) cos (\frac{π}{4}) - cos (x) sin (\frac{π}{4})

cos (\frac{π}{4})

단순화하세요:

\frac{2}{2}

cos (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{4}) = \frac{2}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} sin (x) - sin (\frac{π}{4}) cos (x)

sin (\frac{π}{4})

단순화하세요:

\frac{2}{2}

sin (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{4}) = \frac{2}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} sin (x) - \frac{2}{2} cos (x)

= \frac{\frac{2}{2} sin ( x ) - \frac{2}{2} cos ( x )}{cos ( \frac{π}{4} ) cos ( x ) + sin ( \frac{π}{4} ) sin ( x )}

cos (x) cos (\frac{π}{4}) + sin (x) sin (\frac{π}{4}) = \frac{2}{2} cos (x) + \frac{2}{2} sin (x)

cos (x) cos (\frac{π}{4}) + sin (x) sin (\frac{π}{4})

cos (\frac{π}{4})

단순화하세요:

\frac{2}{2}

cos (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{4}) = \frac{2}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} cos (x) + sin (\frac{π}{4}) sin (x)

sin (\frac{π}{4})

단순화하세요:

\frac{2}{2}

sin (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{4}) = \frac{2}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} cos (x) + \frac{2}{2} sin (x)

= \frac{\frac{2}{2} sin ( x ) - \frac{2}{2} cos ( x )}{\frac{2}{2} cos ( x ) + \frac{2}{2} sin ( x )}

cos (x) \frac{2}{2}

곱하다

: \frac{2 cos ( x )}{2}

cos (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( x )}{2}

= \frac{\frac{2}{2} sin ( x ) - \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} + \frac{2}{2} sin ( x )}

sin (x) \frac{2}{2}

곱하다

: \frac{2 sin ( x )}{2}

sin (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( x )}{2}

= \frac{\frac{2}{2} sin ( x ) - \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} + \frac{2 s i n ( x )}{2}}

sin (x) \frac{2}{2}

곱하다

: \frac{2 sin ( x )}{2}

sin (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} - \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} + \frac{2 s i n ( x )}{2}}

cos (x) \frac{2}{2}

곱하다

: \frac{2 cos ( x )}{2}

cos (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} - \frac{2 c o s ( x )}{2}}{\frac{2 c o s ( x )}{2} + \frac{2 s i n ( x )}{2}}

분수를 합치다

\frac{2 cos ( x )}{2} + \frac{2 sin ( x )}{2} : \frac{2 cos ( x ) + 2 sin ( x )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 cos ( x ) + 2 sin ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} - \frac{2 c o s ( x )}{2}}{\frac{2 c o s ( x ) + 2 s i n ( x )}{2}}

분수를 합치다

\frac{2 sin ( x )}{2} - \frac{2 cos ( x )}{2} : \frac{2 sin ( x ) - 2 cos ( x )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 sin ( x ) - 2 cos ( x )}{2}

= \frac{\frac{2 s i n ( x ) - 2 c o s ( x )}{2}}{\frac{2 c o s ( x ) + 2 s i n ( x )}{2}}

분수 나누기:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 2 sin ( x ) - 2 cos ( x ) ) \cdot 2}{2 ( 2 cos ( x ) + 2 sin ( x ) )}

공통 요인 취소:

2

= \frac{2 sin ( x ) - 2 cos ( x )}{2 cos ( x ) + 2 sin ( x )}

공통 용어를 추출하다

2

= \frac{2 ( sin ( x ) - cos ( x ) )}{2 cos ( x ) + 2 sin ( x )}

공통 용어를 추출하다

2

= \frac{2 ( sin ( x ) - cos ( x ) )}{2 ( cos ( x ) + sin ( x ) )}

공통 요인 취소:

2

= \frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )}

= \frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )}

기본 삼각형 항등식 사용:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x + \frac{π}{4} )}{cos ( x + \frac{π}{4} )}

앵글섬식별사용:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= \frac{sin ( x ) cos ( \frac{π}{4} ) + cos ( x ) sin ( \frac{π}{4} )}{cos ( x + \frac{π}{4} )}

앵글섬식별사용:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= \frac{sin ( x ) cos ( \frac{π}{4} ) + cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) - sin ( x ) sin ( \frac{π}{4} )}

\frac{sin ( x ) cos ( \frac{π}{4} ) + cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) - sin ( x ) sin ( \frac{π}{4} )}

단순화하세요:

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )}

\frac{sin ( x ) cos ( \frac{π}{4} ) + cos ( x ) sin ( \frac{π}{4} )}{cos ( x ) cos ( \frac{π}{4} ) - sin ( x ) sin ( \frac{π}{4} )}

sin (x) cos (\frac{π}{4}) + cos (x) sin (\frac{π}{4}) = \frac{2}{2} sin (x) + \frac{2}{2} cos (x)

sin (x) cos (\frac{π}{4}) + cos (x) sin (\frac{π}{4})

cos (\frac{π}{4})

단순화하세요:

\frac{2}{2}

cos (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{4}) = \frac{2}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} sin (x) + sin (\frac{π}{4}) cos (x)

sin (\frac{π}{4})

단순화하세요:

\frac{2}{2}

sin (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{4}) = \frac{2}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} sin (x) + \frac{2}{2} cos (x)

= \frac{\frac{2}{2} sin ( x ) + \frac{2}{2} cos ( x )}{cos ( \frac{π}{4} ) cos ( x ) - sin ( \frac{π}{4} ) sin ( x )}

cos (x) cos (\frac{π}{4}) - sin (x) sin (\frac{π}{4}) = \frac{2}{2} cos (x) - \frac{2}{2} sin (x)

cos (x) cos (\frac{π}{4}) - sin (x) sin (\frac{π}{4})

cos (\frac{π}{4})

단순화하세요:

\frac{2}{2}

cos (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{4}) = \frac{2}{2}

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} cos (x) - sin (\frac{π}{4}) sin (x)

sin (\frac{π}{4})

단순화하세요:

\frac{2}{2}

sin (\frac{π}{4})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{4}) = \frac{2}{2}

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} cos (x) - \frac{2}{2} sin (x)

= \frac{\frac{2}{2} sin ( x ) + \frac{2}{2} cos ( x )}{\frac{2}{2} cos ( x ) - \frac{2}{2} sin ( x )}

cos (x) \frac{2}{2}

곱하다

: \frac{2 cos ( x )}{2}

cos (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( x )}{2}

= \frac{\frac{2}{2} sin ( x ) + \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} - \frac{2}{2} sin ( x )}

sin (x) \frac{2}{2}

곱하다

: \frac{2 sin ( x )}{2}

sin (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( x )}{2}

= \frac{\frac{2}{2} sin ( x ) + \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} - \frac{2 s i n ( x )}{2}}

sin (x) \frac{2}{2}

곱하다

: \frac{2 sin ( x )}{2}

sin (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} + \frac{2}{2} cos ( x )}{\frac{2 c o s ( x )}{2} - \frac{2 s i n ( x )}{2}}

cos (x) \frac{2}{2}

곱하다

: \frac{2 cos ( x )}{2}

cos (x) \frac{2}{2}

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} + \frac{2 c o s ( x )}{2}}{\frac{2 c o s ( x )}{2} - \frac{2 s i n ( x )}{2}}

분수를 합치다

\frac{2 cos ( x )}{2} - \frac{2 sin ( x )}{2} : \frac{2 cos ( x ) - 2 sin ( x )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 cos ( x ) - 2 sin ( x )}{2}

= \frac{\frac{2 s i n ( x )}{2} + \frac{2 c o s ( x )}{2}}{\frac{2 c o s ( x ) - 2 s i n ( x )}{2}}

분수를 합치다

\frac{2 sin ( x )}{2} + \frac{2 cos ( x )}{2} : \frac{2 sin ( x ) + 2 cos ( x )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 sin ( x ) + 2 cos ( x )}{2}

= \frac{\frac{2 s i n ( x ) + 2 c o s ( x )}{2}}{\frac{2 c o s ( x ) - 2 s i n ( x )}{2}}

분수 나누기:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 2 sin ( x ) + 2 cos ( x ) ) \cdot 2}{2 ( 2 cos ( x ) - 2 sin ( x ) )}

공통 요인 취소:

2

= \frac{2 sin ( x ) + 2 cos ( x )}{2 cos ( x ) - 2 sin ( x )}

공통 용어를 추출하다

2

= \frac{2 ( sin ( x ) + cos ( x ) )}{2 cos ( x ) - 2 sin ( x )}

공통 용어를 추출하다

2

= \frac{2 ( sin ( x ) + cos ( x ) )}{2 ( cos ( x ) - sin ( x ) )}

공통 요인 취소:

2

= \frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )}

= \frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )}

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )} - \frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )} = 3

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )} - \frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )}

단순화하세요:

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )} - \frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )}

cos (x) - sin (x), cos (x) + sin (x)

의 최소 공배수:

(cos (x) - sin (x)) (cos (x) + sin (x))

cos (x) - sin (x), cos (x) + sin (x)

최저공통승수 (LCM)

다음 중 하나에 나타나는 요인으로 구성된 식을 계산합니다

cos (x) - sin (x)

혹은

cos (x) + sin (x)

= (cos (x) - sin (x)) (cos (x) + sin (x))

LCM을 기준으로 분수 조정

각 분자를 곱하는 데 필요한 동일한 양으로 곱하시오

해당 분모를 LCM으로 변환합니다

(cos (x) - sin (x)) (cos (x) + sin (x))

위해서

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )} :

분모와 분자를 곱하다

cos (x) + sin (x)

\frac{sin ( x ) + cos ( x )}{cos ( x ) - sin ( x )} = \frac{( sin ( x ) + cos ( x ) ) ( cos ( x ) + sin ( x ) )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} = \frac{( sin ( x ) + cos ( x ) ) ^{2}}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

위해서

\frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )} :

분모와 분자를 곱하다

cos (x) - sin (x)

\frac{sin ( x ) - cos ( x )}{cos ( x ) + sin ( x )} = \frac{( sin ( x ) - cos ( x ) ) ( cos ( x ) - sin ( x ) )}{( cos ( x ) + sin ( x ) ) ( cos ( x ) - sin ( x ) )}

= \frac{( sin ( x ) + cos ( x ) ) ^{2}}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} - \frac{( sin ( x ) - cos ( x ) ) ( cos ( x ) - sin ( x ) )}{( cos ( x ) + sin ( x ) ) ( cos ( x ) - sin ( x ) )}

분모가 같기 때문에, 분수를 합친다:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{( sin ( x ) + cos ( x ) ) ^{2} - ( sin ( x ) - cos ( x ) ) ( cos ( x ) - sin ( x ) )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

(sin (x) + cos (x))^{2} - (sin (x) - cos (x)) (cos (x) - sin (x))

확대한다:

2 sin^{2} (x) + 2 cos^{2} (x)

(sin (x) + cos (x))^{2} - (sin (x) - cos (x)) (cos (x) - sin (x))

(sin (x) + cos (x))^{2} : sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x)

완벽한 정사각형 공식 적용:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = sin (x), b = cos (x)

= sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x)

= sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x) - (sin (x) - cos (x)) (cos (x) - sin (x))

- (sin (x) - cos (x)) (cos (x) - sin (x))

확대한다:

- 2 cos (x) sin (x) + sin^{2} (x) + cos^{2} (x)

(sin (x) - cos (x)) (cos (x) - sin (x))

확대한다:

2 cos (x) sin (x) - sin^{2} (x) - cos^{2} (x)

(sin (x) - cos (x)) (cos (x) - sin (x))

호일 방법 적용:

(a + b) (c + d) = a c + a d + b c + b d

a = sin (x), b = - cos (x), c = cos (x), d = - sin (x)

= sin (x) cos (x) + sin (x) (- sin (x)) + (- cos (x)) cos (x) + (- cos (x)) (- sin (x))

마이너스 플러스 규칙 적용

+ (- a) = - a, (- a) (- b) = ab

= sin (x) cos (x) - sin (x) sin (x) - cos (x) cos (x) + cos (x) sin (x)

sin (x) cos (x) - sin (x) sin (x) - cos (x) cos (x) + cos (x) sin (x)

단순화하세요:

2 cos (x) sin (x) - sin^{2} (x) - cos^{2} (x)

sin (x) cos (x) - sin (x) sin (x) - cos (x) cos (x) + cos (x) sin (x)

유사 요소 추가:

sin (x) cos (x) + cos (x) sin (x) = 2 cos (x) sin (x)

= 2 cos (x) sin (x) - sin (x) sin (x) - cos (x) cos (x)

sin (x) sin (x) = sin^{2} (x)

sin (x) sin (x)

지수 규칙 적용:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

숫자 추가:

1 + 1 = 2

= sin^{2} (x)

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

지수 규칙 적용:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

숫자 추가:

1 + 1 = 2

= cos^{2} (x)

= 2 cos (x) sin (x) - sin^{2} (x) - cos^{2} (x)

= 2 cos (x) sin (x) - sin^{2} (x) - cos^{2} (x)

= - (2 cos (x) sin (x) - sin^{2} (x) - cos^{2} (x))

괄호 배포

= - (2 cos (x) sin (x)) - (- sin^{2} (x)) - (- cos^{2} (x))

마이너스 플러스 규칙 적용

- (- a) = a, - (a) = - a

= - 2 cos (x) sin (x) + sin^{2} (x) + cos^{2} (x)

= sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x) - 2 cos (x) sin (x) + sin^{2} (x) + cos^{2} (x)

sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x) - 2 cos (x) sin (x) + sin^{2} (x) + cos^{2} (x)

단순화하세요:

2 sin^{2} (x) + 2 cos^{2} (x)

sin^{2} (x) + 2 sin (x) cos (x) + cos^{2} (x) - 2 cos (x) sin (x) + sin^{2} (x) + cos^{2} (x)

유사 요소 추가:

2 sin (x) cos (x) - 2 cos (x) sin (x) = 0

= sin^{2} (x) + cos^{2} (x) + sin^{2} (x) + cos^{2} (x)

유사 요소 추가:

cos^{2} (x) + cos^{2} (x) = 2 cos^{2} (x)

= sin^{2} (x) + 2 cos^{2} (x) + sin^{2} (x)

유사 요소 추가:

sin^{2} (x) + sin^{2} (x) = 2 sin^{2} (x)

= 2 sin^{2} (x) + 2 cos^{2} (x)

= 2 sin^{2} (x) + 2 cos^{2} (x)

= \frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} = 3

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} = 3

빼다

3

양쪽에서

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} - 3 = 0

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} - 3

단순화하세요:

\frac{5 sin ^{2} ( x ) - cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

\frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} - 3

요소를 분수로 변환:

3 = \frac{3 ( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

= \frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} - \frac{3 ( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

분모가 같기 때문에, 분수를 합친다:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 sin ^{2} ( x ) + 2 cos ^{2} ( x ) - 3 ( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

2 sin^{2} (x) + 2 cos^{2} (x) - 3 (cos (x) - sin (x)) (cos (x) + sin (x))

확대한다:

5 sin^{2} (x) - cos^{2} (x)

2 sin^{2} (x) + 2 cos^{2} (x) - 3 (cos (x) - sin (x)) (cos (x) + sin (x))

- 3 (cos (x) - sin (x)) (cos (x) + sin (x))

확대한다:

- 3 cos^{2} (x) + 3 sin^{2} (x)

(cos (x) - sin (x)) (cos (x) + sin (x))

확대한다:

cos^{2} (x) - sin^{2} (x)

(cos (x) - sin (x)) (cos (x) + sin (x))

두 제곱 공식의 차이 적용:

(a - b) (a + b) = a^{2} - b^{2}

a = cos (x), b = sin (x)

= cos^{2} (x) - sin^{2} (x)

= - 3 (cos^{2} (x) - sin^{2} (x))

- 3 (cos^{2} (x) - sin^{2} (x))

확대한다:

- 3 cos^{2} (x) + 3 sin^{2} (x)

- 3 (cos^{2} (x) - sin^{2} (x))

분배 법칙 적용:

a (b - c) = ab - a c

a = - 3, b = cos^{2} (x), c = sin^{2} (x)

= - 3 cos^{2} (x) - (- 3) sin^{2} (x)

마이너스 플러스 규칙 적용

- (- a) = a

= - 3 cos^{2} (x) + 3 sin^{2} (x)

= - 3 cos^{2} (x) + 3 sin^{2} (x)

= 2 sin^{2} (x) + 2 cos^{2} (x) - 3 cos^{2} (x) + 3 sin^{2} (x)

2 sin^{2} (x) + 2 cos^{2} (x) - 3 cos^{2} (x) + 3 sin^{2} (x)

단순화하세요:

5 sin^{2} (x) - cos^{2} (x)

2 sin^{2} (x) + 2 cos^{2} (x) - 3 cos^{2} (x) + 3 sin^{2} (x)

유사 요소 추가:

2 cos^{2} (x) - 3 cos^{2} (x) = - cos^{2} (x)

= 2 sin^{2} (x) - cos^{2} (x) + 3 sin^{2} (x)

유사 요소 추가:

2 sin^{2} (x) + 3 sin^{2} (x) = 5 sin^{2} (x)

= 5 sin^{2} (x) - cos^{2} (x)

= 5 sin^{2} (x) - cos^{2} (x)

= \frac{5 sin ^{2} ( x ) - cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )}

\frac{5 sin ^{2} ( x ) - cos ^{2} ( x )}{( cos ( x ) - sin ( x ) ) ( cos ( x ) + sin ( x ) )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

5 sin^{2} (x) - cos^{2} (x) = 0

5 sin^{2} (x) - cos^{2} (x)

요인:

(5 sin (x) + cos (x)) (5 sin (x) - cos (x))

5 sin^{2} (x) - cos^{2} (x)

5 sin^{2} (x) - cos^{2} (x) (5 sin (x))^{2} - cos^{2} (x)

로 다시 씁니다

5 sin^{2} (x) - cos^{2} (x)

급진적인 규칙 적용:

a = (a)^{2}

5 = (5)^{2}

= (5)^{2} sin^{2} (x) - cos^{2} (x)

지수 규칙 적용:

a^{m} b^{m} = (ab)^{m}

(5)^{2} sin^{2} (x) = (5 sin (x))^{2}

= (5 sin (x))^{2} - cos^{2} (x)

= (5 sin (x))^{2} - cos^{2} (x)

두 제곱 공식의 차이 적용:

x^{2} - y^{2} = (x + y) (x - y)

(5 sin (x))^{2} - cos^{2} (x) = (5 sin (x) + cos (x)) (5 sin (x) - cos (x))

= (5 sin (x) + cos (x)) (5 sin (x) - cos (x))

(5 sin (x) + cos (x)) (5 sin (x) - cos (x)) = 0

각 부분을 개별적으로 해결

5 sin (x) + cos (x) = 0 or 5 sin (x) - cos (x) = 0

5 sin (x) + cos (x) = 0 : x = arctan (- \frac{5}{5}) + πn

5 sin (x) + cos (x) = 0

삼각성을 사용하여 다시 쓰기

5 sin (x) + cos (x) = 0

cos (x), cos (x) \neq = 0

양쪽을 다음으로 나눕니다

\frac{5 sin ( x ) + cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

단순화

\frac{5 sin ( x )}{cos ( x )} + 1 = 0

기본 삼각형 항등식 사용:

\frac{sin ( x )}{cos ( x )} = tan (x)

5 tan (x) + 1 = 0

5 tan (x) + 1 = 0

1

를 오른쪽으로 이동

5 tan (x) + 1 = 0

빼다

1

양쪽에서

5 tan (x) + 1 - 1 = 0 - 1

단순화

5 tan (x) = - 1

5 tan (x) = - 1

양쪽을 다음으로 나눕니다

5

5 tan (x) = - 1

양쪽을 다음으로 나눕니다

5

\frac{5 tan ( x )}{5} = \frac{- 1}{5}

단순화

\frac{5 tan ( x )}{5} = \frac{- 1}{5}

\frac{5 tan ( x )}{5}

간소화하다 :

tan (x)

\frac{5 tan ( x )}{5}

공통 요인 취소:

5

= tan (x)

\frac{- 1}{5}

간소화하다 :

- \frac{5}{5}

\frac{- 1}{5}

분수 규칙 적용:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{5}

- \frac{1}{5}

합리화합니다 :

- \frac{5}{5}

- \frac{1}{5}

공역에 곱셈

\frac{5}{5}

= - \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

급진적인 규칙 적용:

a a = a

55 = 5

= 5

= - \frac{5}{5}

= - \frac{5}{5}

tan (x) = - \frac{5}{5}

tan (x) = - \frac{5}{5}

tan (x) = - \frac{5}{5}

트리거 역속성 적용

tan (x) = - \frac{5}{5}

일반 솔루션

tan (x) = - \frac{5}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{5}{5}) + πn

x = arctan (- \frac{5}{5}) + πn

5 sin (x) - cos (x) = 0 : x = arctan (\frac{5}{5}) + πn

5 sin (x) - cos (x) = 0

삼각성을 사용하여 다시 쓰기

5 sin (x) - cos (x) = 0

cos (x), cos (x) \neq = 0

양쪽을 다음으로 나눕니다

\frac{5 sin ( x ) - cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

단순화

\frac{5 sin ( x )}{cos ( x )} - 1 = 0

기본 삼각형 항등식 사용:

\frac{sin ( x )}{cos ( x )} = tan (x)

5 tan (x) - 1 = 0

5 tan (x) - 1 = 0

1

를 오른쪽으로 이동

5 tan (x) - 1 = 0

더하다

1

양쪽으로

5 tan (x) - 1 + 1 = 0 + 1

단순화

5 tan (x) = 1

5 tan (x) = 1

양쪽을 다음으로 나눕니다

5

5 tan (x) = 1

양쪽을 다음으로 나눕니다

5

\frac{5 tan ( x )}{5} = \frac{1}{5}

단순화

\frac{5 tan ( x )}{5} = \frac{1}{5}

\frac{5 tan ( x )}{5}

간소화하다 :

tan (x)

\frac{5 tan ( x )}{5}

공통 요인 취소:

5

= tan (x)

\frac{1}{5}

간소화하다 :

\frac{5}{5}

\frac{1}{5}

공역에 곱셈

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

급진적인 규칙 적용:

a a = a

55 = 5

= 5

= \frac{5}{5}

tan (x) = \frac{5}{5}

tan (x) = \frac{5}{5}

tan (x) = \frac{5}{5}

트리거 역속성 적용

tan (x) = \frac{5}{5}

일반 솔루션

tan (x) = \frac{5}{5}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{5}{5}) + πn

x = arctan (\frac{5}{5}) + πn

모든 솔루션 결합

x = arctan (- \frac{5}{5}) + πn, x = arctan (\frac{5}{5}) + πn

해를 10진수 형식으로 표시

x = - 0.42053 \dots + πn, x = 0.42053 \dots + πn

그래프

인기 있는 예

cos(x)(2sin(x)-sqrt(2))=0

cos (x) (2 sin (x) - 2) = 0

2sin^2(θ)-3sin(θ)=-1

2 sin^{2} (θ) - 3 sin (θ) = - 1

cos (kπ) = 0

sin (θ) = - 0.8

cos(x/3-pi/4)= 1/2

cos (\frac{x}{3} - \frac{π}{4}) = \frac{1}{2}