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

解

展開する

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

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

解答ステップ

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

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

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