Question

Solve the following equation:
$\cos x+2\cos 2x=1$

Answer 1

$\cos x+2\cos 2x=1$

$\cos x+2({\cos }^{2}x-1)=1$

${4\cos }^{2}x+\cos x-3=0$

${4\cos }^{2}x+4\cos x-3\cos x-3=0$

$(\cos x+1)(4\cos x-3)=0$

Either, $\cos x=-1$

$x=(2n+1)\pi .$

or, $\cos x=\frac{3}{4}$

$x=2n\pi \pm {\cos }^{-1}\left(\frac{3}{4}\right)$