Question

please solve this question

Answer 1

the answer is in the picture i am uploading

Answer 2

Differentiation by Transformation: Sometimes a substitution facilitates differentiation.

sin-1{$\frac{\sqrt{1+x}+\sqrt{1-x}}{2}$}

put x=cos2a

sin-1{$\frac{\sqrt{2cos^2\alpha}+\sqrt{2sin^2\alpha}}{2}$}

sin-1{$\frac{\sqrt{2cos^2\alpha}+\sqrt{2sin^2\alpha}}{2}$}

sin-1$\sqrt{2}\frac{cos\alpha-sin\alpha}{2}$