Question

prove that sec^2Acosec^2A=tan^2A+cot^2A+2​

Answer 1

LHS=tan ^2 A+cot^2 A+2

=sin^2 A/cos^2 A+cos^2 A/sin^2 A+2

=(sin^4 A+cos^4A+2.sin^2 A. cos^2 A)/sin^2A. cos^2 A

=[(sin^2 A+cos^2 A) ^2] /sin^2A. cos^2 A

=[(1)^2] /sin^2 A. cos ^2 A

=1/sin^2 A. cos^2 A

=1/sin^2 A.1/ cos^2 A

=cosec^2 A. sec^2 A

=RHS

So, LHS=RHS(proved)

Hope it would be helpful for you!