Question

$\int \cos x\cdot \cos \left(\sin x\right)dx$ is equal to
(where $C$ is constant of integration)

• A. $\cos \left(\sin x\right)+C$
• B. $\sin \left(\sin x\right)+C$
• C. $\sin \left(\cos x\right)+C$
• D. $\cos \left(\cos x\right)+C$

Answer 1

The correct option is B $\sin \left(\sin x\right)+C$

$I=\int \cos x\cdot \cos \left(\sin x\right)dx$
Putting $\sin x=t$
$\Rightarrow \cos xdx=dt$
$\therefore I=\int \cos tdt=\sin t+C=\sin \left(\sin x\right)+C$