Question

tan^2A + cot^2A = sec^2Acosec^2A - 2

Answer 1

LHS=tan2A+cot2A
=sin2A/cos2A +cos2A/sin2A
= sin4A+cos4A/sin2A.cos2A
=(sin2A+cos2A)^2-2sin2Acos2A/
sin2Acos2A
=1-2sin2Acos2A/ cos2Asin2A
=sec2Atan2A-2

Answer 2

Answer:

Step-by-step explanation:

LHS=tan^2 A+cot^2A

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

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

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

=(1) ^2 - 2sin^2 A. cos^2 A/cos^2 A. sin^2 A

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

=(1/cos^2 A. sin^2 A)-(2/2sin^2 A. cos^2 A)

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

=sec^2 A. cosec^2 A-2

RHS=sec^2 A. cosec^2 A-2

So LHS=RHS(proved).