If $y=\sqrt{\frac{1+\cos 2\theta }{1-\cos 2\theta }}\text{ then }\frac{dy}{d\theta }\text{ at }\theta =\frac{3\pi }{4}$ is

$y=\sqrt{\frac{1+\cos 2\theta }{1-\cos 2\theta }}=\sqrt{\frac{2{\cos }^2\theta }{2{\sin }^2\theta }}=\left|cot\theta \right|$

$at \theta =\frac{3\pi }{4}, y=|\cot \theta |=-\cot \theta$

$\frac{dy}{d\theta }=\cos e{c}^2\theta$

$\frac{dy}{d\theta }\text{ at }\theta =\frac{3\pi }{4} \mathrm{is} {\mathrm{cosec}}^2\frac{3\mathrm{\pi }}{4}=2$