展開する (2sin^2(x)-cos(x)(1-2cos(x)))/(sin^2(x))

解

展開する

\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 )}

解答ステップ

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

拡張

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 )}

分数の規則を適用する:

\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 )}

キャンセル

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

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