Prove.

\(\sec^2 a + cosec ^ 2 a = Sec^2 a. Cosec^2 a\)

Proof ::

LHS = sec^{2} A + cosec^{2} A

\(={1\over(cos^2A)}+{1\over(sin^2A)}={(sin^2A+cos^2A)\over(cos^2A sin^2A)}\)

\(={1\over(cos^2A sin^2A)}=sec^2A cosec^2A=RHS\)