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

解答

展开

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

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

求解步骤

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

乘开

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

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

使用分式法则:

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

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

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

消掉

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

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

e x p an d A (- 2, - 1) B (- 4, 1) c (- 1, 4)

s im pl i f y (x + \frac{1}{4}) (x - 5)

e x p an d (x^{3} + 4 x^{2}) + (3 x^{2} + 12 x) i

e x p an d \frac{( 1 - e ^{- a t} )}{( z - 1 ) ( z - e ^{- a t} )}

e x p an d \frac{( x + 1 ) ( x + 1 )}{x + 2 x + 1}