Question

Solve: $\int \cos x\cos 2xdx,x\in R$

Answer 1

$\int \cos x\cos 2xdx$

$\Rightarrow \frac{1}{2}\int 2\cos x\cos 2xdx$ $\because 2\cos a.\cos b=\cos (a+b)+\cos (a+b)$

$\Rightarrow \frac{1}{2}\int (\cos x+\cos 3x)dx$

$\Rightarrow \frac{1}{2}\int \cos xdx+\frac{1}{2}\int \cos 3xdx$

$=-\frac{\cos x}{2}-\frac{\cos 3x}{6}+c$