Prove the following

Question:

If $2 y=\left(\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right)^{2}, x \in\left(0, \frac{\pi}{2}\right)$

then $\frac{d y}{d x}$ is equal to :

  1. $2 x-\frac{\pi}{3}$

  2. $\frac{\pi}{3}-x$

  3. $\frac{\pi}{6}-x$

  4. $x-\frac{\pi}{6}$


Correct Option: 4,

Solution:

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