Question

Find the domain of definition of the following function:
$y=\frac{1}{\sqrt{4\cos x+1}}$

Answer 1

$4\cos x+1>0$

$\cos x>-\frac{1}{4}$

$\therefore$ $x\in \left[\right(2n-1)\frac{\pi }{2}-{\cos }^{-1}(\frac{1}{4}),(2n+1)\frac{\pi }{2}+{\cos }^{-1}(\frac{1}{4}\left)\right].$