Mathematics - Differentiation Question with Solution | TestHub

$y=\sqrt{\frac{1+\cos 2\theta }{1-\cos 2\theta }}$
$\Rightarrow y=\sqrt{\frac{2{\cos }^2\theta }{2{\sin }^2\theta }}=\sqrt{{\cot }^2\theta }$
$\Rightarrow y=\cot \theta$
Differentiate w.r.t. ' $\theta$ ', we get: $\frac{dy}{d\theta }=-{\mathrm{cosec}}^2\theta$
Now, ${\left(\frac{\mathrm{dy}}{\mathrm{d}\theta }\right)}_{\theta =\frac{3\pi }{4}}=-{\mathrm{cosec}}^2\left(\frac{3\pi }{4}\right)$
$=-{\mathrm{cosec}}^2\left(\pi -\frac{\pi }{4}\right)=-{\mathrm{cosec}}^2\frac{\pi }{4}=-2$