Question

Integrate the following function$\frac{\cos x}{\sqrt{4-{\sin }^2}x}$

Answer 1

Put, $\sin x=t⟹\cos xdx=dt$

$\int \frac{\cos x}{\sqrt{4-{\sin }^{2}x}}dx$

$=\int \frac{1}{\sqrt{2^2-t^2}}dt$

$={\sin }^{-1}\left(\frac{t}{2}\right)+c$

$={\sin }^{-1}\left(\frac{\sin x}{2}\right)+c$ (Ans)