Question

$\int \sin x\sin \left(\cos x\right)dx$

Answer 1

$I=\int \sin x\sin \left(\cos x\right)dx$

Putting $\cos x=t$

differentiating both sides,

$-\sin xdx=dt$

and substituting the values,

$I=-\int \sin tdt=-(-\cos t)=\cos t$

$=\cos \left(\cos x\right)[\therefore \cos x=t]$