Answer
The identity is verified.
$\frac{cot^2t}{csc~t}=\frac{1-sin^2t}{sin~t}$
Work Step by Step
$sin^2t+cos^2t=1$
$cos^2t=1-sin^2t$
$\frac{cot^2t}{csc~t}=\frac{\frac{cos^2t}{sin^2t}}{\frac{1}{sin~t}}=\frac{cos^2t}{sin^2t}\frac{sin~t}{1}=\frac{cos^2t}{sin~t}=\frac{1-sin^2t}{sin~t}$
