Question

Solve the equation on the interval [0,2π). cos^4x=cos^4xcscx

Answer 1

$\cos^4x=\cos^4x\csc x$
$\cos^4x-\cos^4x\csc x=0$
$\cos^4x(1-\csc x)=0$
$\implies \begin{cases}\cos^4x=0\\1-\csc x=0\end{cases}\implies x=\dfrac\pi2,\dfrac{3\pi}2$