Question

Find the range of $f\left(x\right)={\cos }^{4}x+{\sin }^{2}x-1$

Answer 1

$f\left(x\right)={\cos }^{4}x+{\sin }^{2}x-1\Rightarrow {\cos }^{4}x+{\cos }^{2}x=0\Rightarrow {\cos }^{2}x({\cos }^{2}x+1)=0$
$\Rightarrow {\cos }^{2}x=0$ or ${\cos }^{2}x\ne -1$
$\Rightarrow x=2n\pi$