# How do you verify (1-sin^2Ѳ)(1+cot^2Ѳ)=cot^2Ѳ?

$f \left(t\right) = \left(1 - {\sin}^{2} t\right) \left(1 + {\cot}^{2} t\right)$
$\left(1 - {\sin}^{2} t\right) = {\cos}^{2} t$
$\left(1 + {\cos}^{2} \frac{t}{\sin} ^ 2 t\right) = \frac{{\sin}^{2} t + {\cos}^{2} t}{{\sin}^{2} t} = \frac{1}{\sin} ^ 2 t$
$f \left(t\right) = \left({\cos}^{2} t\right) \left(\frac{1}{\sin} ^ 2 t\right) = {\cot}^{2} t$ Proved