A) \[\frac{1}{2}\]
B) \[0\]
C) \[\frac{x}{2}\]
D) \[-\frac{1}{2}\]
E) \[-\frac{x}{2}\]
Correct Answer: D
Solution :
\[y={{\cot }^{-1}}\left( \tan \frac{x}{2} \right)\] \[y={{\cot }^{-1}}\cot \left( \frac{\pi }{2}-\frac{x}{2} \right)\] \[y=\frac{\pi }{2}-\frac{x}{2}\] Differentiating w.r.t.\[x\]on both sides, \[\frac{dy}{dx}=-\frac{1}{2}\]
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