展開する-(cos(θ)(-cos(θ)+2)-sin^2(θ))/(2sin(θ))

解

展開する

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

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

解答ステップ

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

拡張

cos (θ) (- cos (θ) + 2) - sin^{2} (θ) : - cos^{2} (θ) + 2 cos (θ) - sin^{2} (θ)

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

簡素化

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

= - \frac{2 cos ( θ ) - 1}{2 sin ( θ )}

分数の規則を適用する:

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

\frac{2 cos ( θ ) - 1}{2 sin ( θ )} = - (\frac{2 cos ( θ )}{2 sin ( θ )}) - (- \frac{1}{2 sin ( θ )})

= - (\frac{2 cos ( θ )}{2 sin ( θ )}) - (- \frac{1}{2 sin ( θ )})

括弧を削除する:

(a) = a, - (- a) = a

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

数を割る:

\frac{2}{2} = 1

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