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人気のある三角関数 >

arcsin(x)+arcsin(sqrt(3)x)= pi/2

解

arcsin (x) + arcsin (3 x) = \frac{π}{2}

解

x = \frac{1}{2}

解答ステップ

arcsin (x) + arcsin (3 x) = \frac{π}{2}

三角関数の公式を使用して書き換える

arcsin (x) + arcsin (3 x)

和・積の公式を使用する:

arcsin (s) + arcsin (t) = arcsin (s 1 - t^{2} + t 1 - s^{2})

= arcsin (x 1 - (3 x)^{2} + 3 x 1 - x^{2})

arcsin (x 1 - (3 x)^{2} + 3 x 1 - x^{2}) = \frac{π}{2}

三角関数の逆数プロパティを適用する

arcsin (x 1 - (3 x)^{2} + 3 x 1 - x^{2}) = \frac{π}{2}

arcsin (x) = a \Rightarrow x = sin (a)

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = sin (\frac{π}{2})

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

次の自明恒等式を使用する:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (x)

2 πn

循環を含む周期性テーブル:

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}

= 1

= 1

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

解く

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1 : x = \frac{1}{2}

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

平方根を削除する

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

両辺から

3 x 1 - x^{2}

を引く

x 1 - (3 x)^{2} + 3 x 1 - x^{2} - 3 x 1 - x^{2} = 1 - 3 x 1 - x^{2}

簡素化

1 - (3 x)^{2} x = 1 - 3 x 1 - x^{2}

両辺を2乗する:

x^{2} - 3 x^{4} = 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

(1 - (3 x)^{2} x)^{2} = (1 - 3 x 1 - x^{2})^{2}

拡張

(1 - (3 x)^{2} x)^{2} : x^{2} - 3 x^{4}

(1 - (3 x)^{2} x)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= x^{2} (1 - (3 x)^{2})^{2}

(1 - (3 x)^{2})^{2} : 1 - (3 x)^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((1 - (3 x)^{2})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (1 - (3 x)^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 1 - (3 x)^{2}

= (1 - (3 x)^{2}) x^{2}

拡張

(1 - (3 x)^{2}) x^{2} : x^{2} - 3 x^{4}

(1 - (3 x)^{2}) x^{2}

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

(3 x)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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

(3)^{2} : 3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

= 3 x^{2}

= x^{2} (- 3 x^{2} + 1)

= x^{2} (1 - 3 x^{2})

分配法則を適用する:

a (b - c) = ab - a c

a = x^{2}, b = 1, c = 3 x^{2}

= x^{2} \cdot 1 - x^{2} \cdot 3 x^{2}

= 1 \cdot x^{2} - 3 x^{2} x^{2}

簡素化

1 \cdot x^{2} - 3 x^{2} x^{2} : x^{2} - 3 x^{4}

1 \cdot x^{2} - 3 x^{2} x^{2}

1 \cdot x^{2} = x^{2}

1 \cdot x^{2}

乗算:

1 \cdot x^{2} = x^{2}

= x^{2}

3 x^{2} x^{2} = 3 x^{4}

3 x^{2} x^{2}

指数の規則を適用する:

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

x^{2} x^{2} = x^{2 + 2}

= 3 x^{2 + 2}

数を足す:

2 + 2 = 4

= 3 x^{4}

= x^{2} - 3 x^{4}

= x^{2} - 3 x^{4}

= x^{2} - 3 x^{4}

拡張

(1 - 3 x 1 - x^{2})^{2} : 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

(1 - 3 x 1 - x^{2})^{2}

= (1 - 3 1 - x^{2} x)^{2}

完全平方式を適用する:

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

a = 1, b = 3 x 1 - x^{2}

= 1^{2} - 2 \cdot 1 \cdot 3 x 1 - x^{2} + (3 x 1 - x^{2})^{2}

簡素化

1^{2} - 2 \cdot 1 \cdot 3 x 1 - x^{2} + (3 x 1 - x^{2})^{2} : 1 - 23 1 - x^{2} x + 31 - x^{2} x^{2}

1^{2} - 2 \cdot 1 \cdot 3 x 1 - x^{2} + (3 x 1 - x^{2})^{2}

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 2 \cdot 1 \cdot 3 1 - x^{2} x + (3 1 - x^{2} x)^{2}

2 \cdot 1 \cdot 3 x 1 - x^{2} = 23 1 - x^{2} x

2 \cdot 1 \cdot 3 x 1 - x^{2}

数を乗じる:

2 \cdot 1 = 2

= 23 1 - x^{2} x

(3 x 1 - x^{2})^{2} = 31 - x^{2} x^{2}

(3 x 1 - x^{2})^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= (3)^{2} x^{2} (1 - x^{2})^{2}

(3)^{2} : 3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

= 3 x^{2} (1 - x^{2})^{2}

(1 - x^{2})^{2} : 1 - x^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((1 - x^{2})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (1 - x^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 1 - x^{2}

= 3 x^{2} (1 - x^{2})

= 1 - 23 1 - x^{2} x + 3 (1 - x^{2}) x^{2}

= 1 - 23 1 - x^{2} x + 3 (1 - x^{2}) x^{2}

拡張

1 - 23 1 - x^{2} x + 3 (1 - x^{2}) x^{2} : 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

1 - 23 1 - x^{2} x + 3 (1 - x^{2}) x^{2}

= 1 - 23 x 1 - x^{2} + 3 x^{2} (1 - x^{2})

拡張

3 x^{2} (1 - x^{2}) : 3 x^{2} - 3 x^{4}

3 x^{2} (1 - x^{2})

分配法則を適用する:

a (b - c) = ab - a c

a = 3 x^{2}, b = 1, c = x^{2}

= 3 x^{2} \cdot 1 - 3 x^{2} x^{2}

= 3 \cdot 1 \cdot x^{2} - 3 x^{2} x^{2}

簡素化

3 \cdot 1 \cdot x^{2} - 3 x^{2} x^{2} : 3 x^{2} - 3 x^{4}

3 \cdot 1 \cdot x^{2} - 3 x^{2} x^{2}

3 \cdot 1 \cdot x^{2} = 3 x^{2}

3 \cdot 1 \cdot x^{2}

数を乗じる:

3 \cdot 1 = 3

= 3 x^{2}

3 x^{2} x^{2} = 3 x^{4}

3 x^{2} x^{2}

指数の規則を適用する:

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

x^{2} x^{2} = x^{2 + 2}

= 3 x^{2 + 2}

数を足す:

2 + 2 = 4

= 3 x^{4}

= 3 x^{2} - 3 x^{4}

= 3 x^{2} - 3 x^{4}

= 1 - 23 1 - x^{2} x + 3 x^{2} - 3 x^{4}

= 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

= 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

x^{2} - 3 x^{4} = 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

x^{2} - 3 x^{4} = 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

両辺から

3 x^{2} - 3 x^{4}

を引く

x^{2} - 3 x^{4} - (3 x^{2} - 3 x^{4}) = 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4} - (3 x^{2} - 3 x^{4})

簡素化

- 2 x^{2} = - 23 1 - x^{2} x + 1

両辺から

1

を引く

- 2 x^{2} - 1 = - 23 1 - x^{2} x + 1 - 1

簡素化

- 2 x^{2} - 1 = - 23 1 - x^{2} x

両辺を2乗する:

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

x^{2} - 3 x^{4} = 1 - 23 x 1 - x^{2} + 3 x^{2} - 3 x^{4}

(- 2 x^{2} - 1)^{2} = (- 23 1 - x^{2} x)^{2}

拡張

(- 2 x^{2} - 1)^{2} : 4 x^{4} + 4 x^{2} + 1

(- 2 x^{2} - 1)^{2}

完全平方式を適用する:

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

a = - 2 x^{2}, b = 1

= (- 2 x^{2})^{2} - 2 (- 2 x^{2}) \cdot 1 + 1^{2}

簡素化

(- 2 x^{2})^{2} - 2 (- 2 x^{2}) \cdot 1 + 1^{2} : 4 x^{4} + 4 x^{2} + 1

(- 2 x^{2})^{2} - 2 (- 2 x^{2}) \cdot 1 + 1^{2}

規則を適用

1^{a} = 1

1^{2} = 1

= (- 2 x^{2})^{2} - 2 \cdot 1 \cdot (- 2 x^{2}) + 1

規則を適用

- (- a) = a

= (- 2 x^{2})^{2} + 2 \cdot 2 x^{2} \cdot 1 + 1

(- 2 x^{2})^{2} = 4 x^{4}

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

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

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

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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

(x^{2})^{2} : x^{4}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= x^{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= x^{4}

= 2^{2} x^{4}

2^{2} = 4

= 4 x^{4}

2 \cdot 2 x^{2} \cdot 1 = 4 x^{2}

2 \cdot 2 x^{2} \cdot 1

数を乗じる:

2 \cdot 2 \cdot 1 = 4

= 4 x^{2}

= 4 x^{4} + 4 x^{2} + 1

= 4 x^{4} + 4 x^{2} + 1

拡張

(- 23 1 - x^{2} x)^{2} : 12 x^{2} - 12 x^{4}

(- 23 1 - x^{2} x)^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 23 1 - x^{2} x)^{2} = (23 1 - x^{2} x)^{2}

= (23 1 - x^{2} x)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} (3)^{2} x^{2} (1 - x^{2})^{2}

(3)^{2} : 3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

= 2^{2} \cdot 3 (1 - x^{2})^{2} x^{2}

(1 - x^{2})^{2} : 1 - x^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((1 - x^{2})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (1 - x^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 1 - x^{2}

= 2^{2} \cdot 3 (1 - x^{2}) x^{2}

改良

= 12 (1 - x^{2}) x^{2}

拡張

12 (1 - x^{2}) x^{2} : 12 x^{2} - 12 x^{4}

12 (1 - x^{2}) x^{2}

= 12 x^{2} (1 - x^{2})

分配法則を適用する:

a (b - c) = ab - a c

a = 12 x^{2}, b = 1, c = x^{2}

= 12 x^{2} \cdot 1 - 12 x^{2} x^{2}

= 12 \cdot 1 \cdot x^{2} - 12 x^{2} x^{2}

簡素化

12 \cdot 1 \cdot x^{2} - 12 x^{2} x^{2} : 12 x^{2} - 12 x^{4}

12 \cdot 1 \cdot x^{2} - 12 x^{2} x^{2}

12 \cdot 1 \cdot x^{2} = 12 x^{2}

12 \cdot 1 \cdot x^{2}

数を乗じる:

12 \cdot 1 = 12

= 12 x^{2}

12 x^{2} x^{2} = 12 x^{4}

12 x^{2} x^{2}

指数の規則を適用する:

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

x^{2} x^{2} = x^{2 + 2}

= 12 x^{2 + 2}

数を足す:

2 + 2 = 4

= 12 x^{4}

= 12 x^{2} - 12 x^{4}

= 12 x^{2} - 12 x^{4}

= 12 x^{2} - 12 x^{4}

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

解く

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4} : x = \frac{1}{2}, x = - \frac{1}{2}

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

12 x^{4}

を左側に移動します

4 x^{4} + 4 x^{2} + 1 = 12 x^{2} - 12 x^{4}

両辺に

12 x^{4}

を足す

4 x^{4} + 4 x^{2} + 1 + 12 x^{4} = 12 x^{2} - 12 x^{4} + 12 x^{4}

簡素化

16 x^{4} + 4 x^{2} + 1 = 12 x^{2}

16 x^{4} + 4 x^{2} + 1 = 12 x^{2}

12 x^{2}

を左側に移動します

16 x^{4} + 4 x^{2} + 1 = 12 x^{2}

両辺から

12 x^{2}

を引く

16 x^{4} + 4 x^{2} + 1 - 12 x^{2} = 12 x^{2} - 12 x^{2}

簡素化

16 x^{4} - 8 x^{2} + 1 = 0

16 x^{4} - 8 x^{2} + 1 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

16 u^{2} - 8 u + 1 = 0

解く

16 u^{2} - 8 u + 1 = 0 : u = \frac{1}{4}

16 u^{2} - 8 u + 1 = 0

解くとthe二次式

16 u^{2} - 8 u + 1 = 0

二次Equationの公式:

次の場合:

a = 16, b = - 8, c = 1

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 16 \cdot 1}{2 \cdot 16}

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 16 \cdot 1}{2 \cdot 16}

(- 8)^{2} - 4 \cdot 16 \cdot 1 = 0

(- 8)^{2} - 4 \cdot 16 \cdot 1

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 8)^{2} = 8^{2}

= 8^{2} - 4 \cdot 16 \cdot 1

数を乗じる:

4 \cdot 16 \cdot 1 = 64

= 8^{2} - 64

8^{2} = 64

= 64 - 64

数を引く:

64 - 64 = 0

= 0

u_{1, 2} = \frac{- ( - 8 ) \pm 0}{2 \cdot 16}

u = \frac{- ( - 8 )}{2 \cdot 16}

\frac{- ( - 8 )}{2 \cdot 16} = \frac{1}{4}

\frac{- ( - 8 )}{2 \cdot 16}

規則を適用

- (- a) = a

= \frac{8}{2 \cdot 16}

数を乗じる:

2 \cdot 16 = 32

= \frac{8}{32}

共通因数を約分する:

8

= \frac{1}{4}

u = \frac{1}{4}

二次equationの解:

u = \frac{1}{4}

u = \frac{1}{4}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{1}{4} : x = \frac{1}{2}, x = - \frac{1}{2}

x^{2} = \frac{1}{4}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

x = \frac{1}{4}, x = - \frac{1}{4}

\frac{1}{4} = \frac{1}{2}

\frac{1}{4}

累乗根の規則を適用する:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

= \frac{1}{4}

累乗根の規則を適用する:

1 = 1

1 = 1

= \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

a^{2} = a, a \geq 0

2^{2} = 2

= 2

= \frac{1}{2}

- \frac{1}{4} = - \frac{1}{2}

- \frac{1}{4}

累乗根の規則を適用する:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

= - \frac{1}{4}

累乗根の規則を適用する:

1 = 1

1 = 1

= - \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

a^{2} = a, a \geq 0

2^{2} = 2

= 2

= - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

解答は

x = \frac{1}{2}, x = - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

解を検算する:

x = \frac{1}{2}

真

, x = - \frac{1}{2}

偽

x 1 - (3 x)^{2} + 3 x 1 - x^{2} = 1

に当てはめて解を確認する

equationに一致しないものを削除する。

挿入

x = \frac{1}{2} :

真

(\frac{1}{2}) 1 - (3 (\frac{1}{2}))^{2} + 3 (\frac{1}{2}) 1 - (\frac{1}{2})^{2} = 1

(\frac{1}{2}) 1 - (3 (\frac{1}{2}))^{2} + 3 (\frac{1}{2}) 1 - (\frac{1}{2})^{2} = 1

(\frac{1}{2}) 1 - (3 (\frac{1}{2}))^{2} + 3 (\frac{1}{2}) 1 - (\frac{1}{2})^{2}

括弧を削除する:

(a) = a

= \frac{1}{2} 1 - (3 \frac{1}{2})^{2} + 3 \frac{1}{2} 1 - (\frac{1}{2})^{2}

\frac{1}{2} 1 - (3 \frac{1}{2})^{2} = \frac{1}{4}

\frac{1}{2} 1 - (3 \frac{1}{2})^{2}

1 - (3 \frac{1}{2})^{2} = \frac{1}{2}

1 - (3 \frac{1}{2})^{2}

(3 \frac{1}{2})^{2} = \frac{3}{4}

(3 \frac{1}{2})^{2}

乗じる

3 \frac{1}{2} : \frac{3}{2}

3 \frac{1}{2}

分数を乗じる:

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

= \frac{1 \cdot 3}{2}

乗算:

1 \cdot 3 = 3

= \frac{3}{2}

= (\frac{3}{2})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 ) ^{2}}{2 ^{2}}

(3)^{2} : 3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

= \frac{3}{2 ^{2}}

2^{2} = 4

= \frac{3}{4}

= 1 - \frac{3}{4}

結合

1 - \frac{3}{4} : \frac{1}{4}

1 - \frac{3}{4}

元を分数に変換する:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{3}{4}

分母が等しいので, 分数を組み合わせる:

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

= \frac{1 \cdot 4 - 3}{4}

1 \cdot 4 - 3 = 1

1 \cdot 4 - 3

数を乗じる:

1 \cdot 4 = 4

= 4 - 3

数を引く:

4 - 3 = 1

= 1

= \frac{1}{4}

= \frac{1}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{1}{2}

規則を適用

1 = 1

= \frac{1}{2}

= \frac{1}{2} \cdot \frac{1}{2}

分数を乗じる:

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

= \frac{1 \cdot 1}{2 \cdot 2}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{1}{4}

3 \frac{1}{2} 1 - (\frac{1}{2})^{2} = \frac{3}{4}

3 \frac{1}{2} 1 - (\frac{1}{2})^{2}

1 - (\frac{1}{2})^{2} = \frac{3}{2}

1 - (\frac{1}{2})^{2}

(\frac{1}{2})^{2} = \frac{1}{4}

(\frac{1}{2})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

規則を適用

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= 1 - \frac{1}{4}

結合

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

元を分数に変換する:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{1}{4}

分母が等しいので, 分数を組み合わせる:

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

= \frac{1 \cdot 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数を乗じる:

1 \cdot 4 = 4

= 4 - 1

数を引く:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= 3 \frac{1}{2} \cdot \frac{3}{2}

分数を乗じる:

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

= \frac{1 \cdot 3 3}{2 \cdot 2}

1 \cdot 33 = 3

1 \cdot 33

累乗根の規則を適用する:

a a = a

33 = 3

= 1 \cdot 3

数を乗じる:

1 \cdot 3 = 3

= 3

= \frac{3}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{3}{4}

= \frac{1}{4} + \frac{3}{4}

規則を適用

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

= \frac{1 + 3}{4}

数を足す:

1 + 3 = 4

= \frac{4}{4}

規則を適用

\frac{a}{a} = 1

= 1

1 = 1

真

挿入

x = - \frac{1}{2} :

偽

(- \frac{1}{2}) 1 - (3 (- \frac{1}{2}))^{2} + 3 (- \frac{1}{2}) 1 - (- \frac{1}{2})^{2} = 1

(- \frac{1}{2}) 1 - (3 (- \frac{1}{2}))^{2} + 3 (- \frac{1}{2}) 1 - (- \frac{1}{2})^{2} = - 1

(- \frac{1}{2}) 1 - (3 (- \frac{1}{2}))^{2} + 3 (- \frac{1}{2}) 1 - (- \frac{1}{2})^{2}

括弧を削除する:

(- a) = - a

= - \frac{1}{2} 1 - (- 3 \frac{1}{2})^{2} - 3 \frac{1}{2} 1 - (- \frac{1}{2})^{2}

\frac{1}{2} 1 - (- 3 \frac{1}{2})^{2} = \frac{1}{4}

\frac{1}{2} 1 - (- 3 \frac{1}{2})^{2}

1 - (- 3 \frac{1}{2})^{2} = \frac{1}{2}

1 - (- 3 \frac{1}{2})^{2}

(- 3 \frac{1}{2})^{2} = \frac{3}{4}

(- 3 \frac{1}{2})^{2}

乗じる

- 3 \frac{1}{2} : - \frac{3}{2}

- 3 \frac{1}{2}

分数を乗じる:

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

= - \frac{1 \cdot 3}{2}

乗算:

1 \cdot 3 = 3

= - \frac{3}{2}

= (- \frac{3}{2})^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- \frac{3}{2})^{2} = (\frac{3}{2})^{2}

= (\frac{3}{2})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 ) ^{2}}{2 ^{2}}

(3)^{2} : 3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

= \frac{3}{2 ^{2}}

2^{2} = 4

= \frac{3}{4}

= 1 - \frac{3}{4}

結合

1 - \frac{3}{4} : \frac{1}{4}

1 - \frac{3}{4}

元を分数に変換する:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{3}{4}

分母が等しいので, 分数を組み合わせる:

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

= \frac{1 \cdot 4 - 3}{4}

1 \cdot 4 - 3 = 1

1 \cdot 4 - 3

数を乗じる:

1 \cdot 4 = 4

= 4 - 3

数を引く:

4 - 3 = 1

= 1

= \frac{1}{4}

= \frac{1}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{1}{2}

規則を適用

1 = 1

= \frac{1}{2}

= \frac{1}{2} \cdot \frac{1}{2}

分数を乗じる:

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

= \frac{1 \cdot 1}{2 \cdot 2}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{1}{4}

3 \frac{1}{2} 1 - (- \frac{1}{2})^{2} = \frac{3}{4}

3 \frac{1}{2} 1 - (- \frac{1}{2})^{2}

1 - (- \frac{1}{2})^{2} = \frac{3}{2}

1 - (- \frac{1}{2})^{2}

(- \frac{1}{2})^{2} = \frac{1}{4}

(- \frac{1}{2})^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- \frac{1}{2})^{2} = (\frac{1}{2})^{2}

= (\frac{1}{2})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

規則を適用

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= 1 - \frac{1}{4}

結合

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

元を分数に変換する:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{1}{4}

分母が等しいので, 分数を組み合わせる:

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

= \frac{1 \cdot 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数を乗じる:

1 \cdot 4 = 4

= 4 - 1

数を引く:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= 3 \frac{1}{2} \cdot \frac{3}{2}

分数を乗じる:

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

= \frac{1 \cdot 3 3}{2 \cdot 2}

1 \cdot 33 = 3

1 \cdot 33

累乗根の規則を適用する:

a a = a

33 = 3

= 1 \cdot 3

数を乗じる:

1 \cdot 3 = 3

= 3

= \frac{3}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{3}{4}

= - \frac{1}{4} - \frac{3}{4}

規則を適用

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

= \frac{- 1 - 3}{4}

数を引く:

- 1 - 3 = - 4

= \frac{- 4}{4}

分数の規則を適用する:

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

= - \frac{4}{4}

規則を適用

\frac{a}{a} = 1

= - 1

- 1 = 1

偽

解は

x = \frac{1}{2}

x = \frac{1}{2}

元のequationに当てはめて解を検算する

arcsin (x) + arcsin (3 x) = \frac{π}{2}

に当てはめて解を確認する

equationに一致しないものを削除する。

解答を確認する

\frac{1}{2} :

真

\frac{1}{2}

挿入

n = 1

\frac{1}{2}

arcsin (x) + arcsin (3 x) = \frac{π}{2}

の挿入向け

x = \frac{1}{2}

arcsin (\frac{1}{2}) + arcsin (3 \frac{1}{2}) = \frac{π}{2}

改良

1.57079 \dots = 1.57079 \dots

\Rightarrow 真

x = \frac{1}{2}

グラフ

人気の例

cos(x)sin(x)= 1/2

cos (x) sin (x) = \frac{1}{2}

(cos(x)-3)(cos(x)+1)=0

(cos (x) - 3) (cos (x) + 1) = 0

4tan^2(x)-16tan(x)+7=0

4 tan^{2} (x) - 16 tan (x) + 7 = 0

1 - cos (x) = 0.5

arctan(100x)-arctan(x)=45

arctan (100 x) - arctan (x) = 4 5^{\circ}