Question

Find the general solution of :

$2\cos x=1$

Answer 1

$2\cos x=1$

This equation is equivalent to $\cos x=\frac{1}{2}$

Now,

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

Hence, the general solution is

$x=\pm \frac{\pi }{3}+2k\pi$, where k is any integer.