11. \( \left(\frac{-\cos ^{2} x}{1+\sin x}\right)+\left(\frac{\sin ^{2} x}{1-\cos x}\right)-\cos x \)
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Answer

\( \frac{-(1+\sin x) +\sin x (1-\cos x)}{(1+\sin x)(1-\cos x)} \)

Steps

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

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

Step 3 ：\( \frac{-(1+\sin x) +\sin x (1-\cos x)}{(1+\sin x)(1-\cos x)} \)