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受欢迎的三角函数 >

cos(pi/4)cos(pi/4)-sin(pi/4)sin(pi/4)

解答

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

解答

0

求解步骤

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

使用以下普通恒等式:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

周期表（周期为

2 πn

）：

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}

使用以下普通恒等式:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (x)

周期表（周期为

2 πn

"）：

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} \cdot \frac{2}{2} - \frac{2}{2} \cdot \frac{2}{2}

化简

\frac{2}{2} \cdot \frac{2}{2} - \frac{2}{2} \cdot \frac{2}{2} : 0

\frac{2}{2} \cdot \frac{2}{2} - \frac{2}{2} \cdot \frac{2}{2}

因式分解出通项

\frac{2}{2}

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

\frac{2}{2} - \frac{2}{2} = 0

\frac{2}{2} - \frac{2}{2}

消掉

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

\frac{2}{2}

消掉

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

\frac{2}{2}

使用根式运算法则:

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

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

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

数字相减:

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

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

使用根式运算法则:

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

= \frac{1}{2}

= \frac{1}{2}

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

消掉

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

\frac{2}{2}

消掉

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

\frac{2}{2}

使用根式运算法则:

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

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

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

数字相减:

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

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

使用根式运算法则:

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

= \frac{1}{2}

= \frac{1}{2}

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

因为分母相等，所以合并分式:

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

= \frac{1 - 1}{2}

数字相减:

1 - 1 = 0

= \frac{0}{2}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

= 0

= 0

流行的例子

cos^2(30)+sin^2(30)