Question

Range of $f\left(x\right)=\frac{1}{1-2\cos x}$ is:

Answer 1

$f\left(x\right)=\frac{1}{1-2\cos x}$

$-1\le \cos x\le 1$

$-2\le 2\cos x\le 2$

$3\le 1-2\cos x\le -1$

$-1\le \frac{1}{1-2\cos x}\le \frac{1}{3}$

so $f\left(x\right)$ has range, $Rϵ[-1,\frac{1}{3}]$.