# How do you prove (1-csc^2t)/ csc^2t = -1/sec^2t?

$\frac{1 - \frac{1}{\sin} ^ 2 t}{\frac{1}{\sin} ^ 2 t} = \frac{1 - {\sin}^{2} t}{\sin} ^ 2 t \left({\sin}^{2} t\right) = - {\cos}^{2} t$.
$\left(- {\cos}^{2} t\right)$ can be written as :$- \frac{1}{\frac{1}{\cos} ^ 2 t} = - \frac{1}{{\sec}^{2} t}$.
$\frac{1 - {\csc}^{2} t}{{\csc}^{2} t} = - \frac{1}{{\sec}^{2} t}$