Solve the following

Question:

If

$y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right)$

then $\frac{d y}{d \alpha}$ at $\alpha=\frac{5 \pi}{6}$ is :

  1. 4

  2. $-\frac{1}{4}$

  3. $\frac{4}{3}$

  4. $-4$


Correct Option: 1

Solution:

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