The integrating factor of sin xdy/dx+2ycos x=4 is :

The correct answer is Option (2) → $|\sin x|^2$

$\sin x\frac{dy}{dx}+2y\cos x=4$

$\frac{dy}{dx}+2y\frac{\cos x}{\sin x}=\frac{4}{\sin x}$ dividing by $\sin x$

$I.F.=e^{\int\frac{2\cos x}{\sin x}}dx=e^{2\log|\sin x|}=|\sin x|^2$