2. We know that $\sec t=\frac{1}{\cos t}$, $\csc t=\frac{1}{\sin t}$ and $\cos^2 t + \sin^2 t =1$ so starting with the LHS:
LHS $=\frac{\sec t}{\cos t}-\frac{\sec^2 t}{\csc^2 t}=\frac{\frac{1}{\cos t}}{\cos t}-\frac{\frac{1}{\cos^2 t}}{\frac{1}{\sin^2 t}}=\frac{1}{\cos^2 t}-\frac{\sin^2 t}{\cos^2 t} =\frac{1-\sin^2 t}{\cos^2 t}=\frac{\cos^2 t}{\cos^2 t}=1=$RHS