A) 0
B) \[-\frac{1}{2}\]
C) ½
D) 1
Correct Answer: B
Solution :
\[y={{\tan }^{-1}}\sqrt{\frac{1+\cos x}{1-\cos x}}={{\tan }^{-1}}\sqrt{\frac{2{{\cos }^{2}}\frac{x}{2}}{2{{\sin }^{2}}\frac{x}{2}}}\] \[={{\tan }^{-1}}\cot \frac{x}{2}={{\tan }^{-1}}\tan \left( \frac{\pi }{2}-\frac{x}{2} \right)=\frac{\pi }{2}-\frac{x}{2}\] Þ \[\frac{dy}{dx}=-\frac{1}{2}\].You need to login to perform this action.
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