Answer
$\cos^{2}x\csc x-\csc x=-\sin x$
Work Step by Step
$\cos^{2}x\csc x-\csc x=-\sin x$
Take out common factor $-\csc x$ from the left side:
$-\csc x(-\cos^{2}x+1)=-\sin x$
Rearrange the expression inside the parentheses:
$-\csc x(1-\cos^{2}x)=-\sin x$
Substitute $\csc x$ by $\dfrac{1}{\sin x}$ and $1-\cos^{2}x$ by $\sin^{2}x$:
$-\Big(\dfrac{1}{\sin x}\Big)(\sin^{2}x)=-\sin x$
Simplify the left side and the identity will be proved:
$-\dfrac{\sin^{2}x}{\sin x}=-\sin x$
$-\sin x=-\sin x$
