Question

Differentiation with respect to x

Answer 1

The solution is attached in the images. The pages are numbered.

The following identities were used:


$\rightarrow \cos 2\theta = 2\cos^2\theta-1 \\ \\ \implies \boxed{1+\cos 2\theta = 2\cos^2\theta} \\ \\ \\ \\ \rightarrow \cos 2\theta = 1-2\sin^2\theta \\ \\ \implies \boxed{1-\cos 2\theta = 2\sin^2\theta} \\ \\ \\ \\ \rightarrow \boxed{\frac{\tan A + \tan B}{1-\tan A \tan B} = \tan (A-B)} \\ \\ \\ \\ \rightarrow \sin^{-1}x + \cos^{-1}x =\frac{\pi}{2} \\ \\ \implies \boxed{\frac{\pi}{2}-\cos^{-1}x=\sin^{-1}x}$