簡約 (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ))

解

簡約

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

- 2 tan^{2} (θ)

解答ステップ

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

結合

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

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

簡素化

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

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

簡素化

\frac{2 sin ^{2} ( θ )}{cos ^{2} ( θ )} : 2 tan^{2} (θ)

= - 2 tan^{2} (θ)