Question

Find $k$ if the equation $2cosx+cos2kx=3$ has only one solution

Answer 1

Given, $2\cos x+\cos 2kx=3$
Solutions exists only when $x=0$
$\therefore \cos x=\cos 2kx=1$
$\cos x=1$ or $\cos 2kx=1$
$\Rightarrow x=2n\pi$ or $x=\frac{2n\pi }{2k}$