Question

Prove that tan2A +cot2A +2=cosec2A sec2A

Answer 1

tan2A + cot2A + 2 = cosec2A sec2A

Take the LHS:

tan2A + cot2A + 2

tan2A + cot2A + 1 + 1

tan2A + 1 + cot2A + 1

Since, tan2A + 1 = sec2A and cot2A + 1 = cosec2A

sec2A + cosec2A

1/cos2A + 1/Sin2A

(Sin2A + Cos2A) / cos2A Sin2A

1/ cos2A sin2A

Sec2A cosec2A= RHS

Answer 2

Answer:

Step-by-step explanation:

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)

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