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

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If \( y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right) \), then \( \frac{d y}{d \alpha} \) at \( \alpha=\frac{5 \pi}{6} \) is
(A) 4
(B) 2
(C) 3
(D) -4
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