#### Answer

$\sin^2\beta(1+\cot^2\beta)=1$

#### Work Step by Step

Start with the left side:
$\sin^2\beta(1+\cot^2\beta)$
Use the identity $1+\cot^2\beta=\csc^2\beta$:
$=\sin^2\beta\csc^2\beta$
$=\sin^2\beta*\frac{1}{\sin^2\beta}$
$=1$
Since this equals the right side, the identity has been proven.