Question

Prove: tan^2A+cot^2A+2=sec^2A*cosec^2A

Answer 1

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L.H.S

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

=(Sin^2Asin^2A+cos^2A.cos^2A+2sin^2A.cos^2A)/sin^2A.cos^2A

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

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

=1/sin^2Acos^2A

=sec^2Acosec^2A

R.H.S proved