If \( y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ...

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If \( y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right) \);
\( \mathrm{P} \) then \( \frac{\mathrm{dy}}{\mathrm{d} \alpha} \) at \( \alpha=\frac{5 \pi}{6} \) is [JEE Main-2020 (January)]

W
(1) 4
(2) \( \frac{4}{3} \)
(3) \( \frac{-1}{4} \)
(4) \( -4 \)
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