Answer
$\csc x\cos^{2}x+\sin x=\csc x$
Work Step by Step
$\csc x\cos^{2}x+\sin x=\csc x$
Substitute $\csc x$ with $\dfrac{1}{\sin x}$:
$\Big(\dfrac{1}{\sin x}\Big)\cos^{2}x+\sin x=\csc x$
Evaluate the sum of fractions on the left side of the equation:
$\dfrac{\cos^{2}x}{\sin x}+\sin x=\csc x$
$\dfrac{\cos^{2}x+\sin^{2}x}{\sin x}=\csc x$
Since $\cos^{2}x+\sin^{2}x=1$, the identity is proved:
$\dfrac{1}{\sin x}=\csc x$
$\csc x=\csc x$
