Question

Solve :- ${\cos }^{-1}\left(\frac{\sqrt{3}\cos x+\sin x}{2}\right)$

Answer 1

${\cos }^{-1}(\frac{\sqrt{3}}{2}\cos x+\frac{1}{2}\sin x)$
$={\cos }^{-1}(\cos \frac{\pi }{6}\cos x+\sin \frac{\pi }{6}\sin x)$
$={\cos }^{-1}\left[\cos (x-\frac{\pi }{6})\right]$
$=x-\frac{\pi }{6}$