# How do you verify the identify sec^2theta-tan^2theta=1?

${\sec}^{2} t = \frac{1}{{\cos}^{2} t}$
$1 - {\sin}^{2} t = {\cos}^{2} t$
$\frac{1}{{\cos}^{2} t} - \frac{{\sin}^{2} t}{{\cos}^{2} t} = \frac{1 - {\sin}^{2} t}{\cos} ^ 2 t = {\cos}^{2} \frac{t}{{\cos}^{2} t} = 1$