Question

Prove the identity

sec^2 θ csc^2θ = csc^2 θ + sec^2 θ

Answer 1

\[
\sec^2 θ \csc^2θ= \frac 1 {\sin^2 x} \frac 1 {\cos^2 x}
\]

Answer 2

\[
\csc^2 θ + \sec^2 θ=\frac 1 {\sin^2 x}+ \frac 1 {\cos^2 x}=\frac {\cos^2 x + sin^2x}{\sin^2(x) \cos^2 x}==\frac {1}{\sin^2(x) \cos^2 x}
\]