Answer
$\dfrac{\cos^{2}v}{\sin v}=\csc v-\sin v$
Work Step by Step
$\dfrac{\cos^{2}v}{\sin v}=\csc v-\sin v$
On the right side of the equation, substitute $\csc v$ with $\dfrac{1}{\sin v}$:
$\dfrac{\cos^{2}v}{\sin v}=\dfrac{1}{\sin v}-\sin v$
Evaluate the difference on the right side of the equation:
$\dfrac{\cos^{2}v}{\sin v}=\dfrac{1-\sin^{2}v}{\sin v}$
Since $1-\sin^{2}v=\cos^{2}v$, this identity is proved:
$\dfrac{\cos^{2}v}{\sin v}=\dfrac{\cos^{2}v}{\sin v}$
