Question

Find the general solution:
$cos3x+cosx-cos2x=0$

Answer 1

$cos3x+cosx-cos2x=0$

$\Rightarrow 2\cos \left(\frac{3x+x}{2}\right)\cos \left(\frac{3x-x}{2}\right)-\cos 2x=0\Rightarrow \cos 2x(2\cos x-1)=0$

$\Rightarrow \cos 2x=0$, $\cos x=\frac{1}{2}$

$\Rightarrow x=\frac{(2n+1)\pi }{4}$, $x=2n\pi \pm \frac{\pi }{3}$