if

$y(\alpha)=\sqrt{\frac{\frac{2 \sin \alpha}{\cos \alpha}+\frac{\cos \alpha}{\sin \alpha}}{\sec ^{2} \alpha}}=\sqrt{\frac{2 \cos ^{2} \alpha}{\sin \alpha \cos \alpha}+\frac{1}{\sin ^{2} \alpha}}$

$=\sqrt{2 \cot \alpha+\operatorname{cosec}^{2} \alpha}=\sqrt{2 \cot \alpha+1+\cot ^{2} \alpha}$

$=|1+\cot \alpha|=-1-\cot \alpha \quad\left[\because \alpha \in\left(\frac{3 \pi}{4}, \pi\right)\right]$

$\frac{d y}{d \alpha}=\operatorname{cosec}^{2} \alpha \Rightarrow\left(\frac{d y}{d \alpha}\right)_{\alpha=\frac{5 \pi}{6}}=4$