展开 (((1-cos(x))^2+sin^2(x)))/(1-cos(x))

解答

展开

\frac{( ( 1 - cos ( x ) ) ^{2} + sin ^{2} ( x ) )}{1 - cos ( x )}

2

求解步骤

\frac{( 1 - cos ( x ) ) ^{2} + sin ^{2} ( x )}{1 - cos ( x )}

乘开

(1 - cos (x))^{2} + sin^{2} (x) : 1 - 2 cos (x) + cos^{2} (x) + sin^{2} (x)

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

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

= \frac{1 - 2 cos ( x ) + 1}{1 - cos ( x )}

1 - 2 cos (x) + 1 = - 2 cos (x) + 2

= \frac{- 2 cos ( x ) + 2}{1 - cos ( x )}

分解

- 2 cos (x) + 2 : 2 (- cos (x) + 1)

= \frac{2 ( - cos ( x ) + 1 )}{1 - cos ( x )}

约分:

- cos (x) + 1

= 2

e x p an d \frac{3 x + 4}{( x + 4 ) ( x ^{2} + x - 4 ) ^{2}}

s im pl i f y (3 1 + x - 1) \cdot (1 + x + 1)

\frac{d}{d y} ((M) (2 x + y))

e x p an d \frac{3600 e ^{- 1.2 t}}{( 1 + 75 e ^{- 1.2 t} ) ^{2}}

s im pl i f y (2 x - 3 y)^{2}