37. (1 tan2 A) +(1+ cot2 A)-(sin2 A - sin4 A)

1.	37. (1 tan2 A) +(1+ cot2 A)-(sin2 A - sin4 A)
Answer» LHS:(1 + tan^2 A) + (1 + cot^2 A)= sec^2 A + cosec^2 A= 1/cos^2 A + 1/sin^2 A= (sin^2 A + cos^2 A) /cos^2 A. sin^2 A= 1/(1 - sin^2 A). sin^2 A= 1/(sin^2 A - sin^4 A)= RHS Hence proved

Answer»

LHS:(1 + tan^2 A) + (1 + cot^2 A)= sec^2 A + cosec^2 A= 1/cos^2 A + 1/sin^2 A= (sin^2 A + cos^2 A) /cos^2 A. sin^2 A= 1/(1 - sin^2 A). sin^2 A= 1/(sin^2 A - sin^4 A)= RHS

Hence proved

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37. (1 tan2 A) +(1+ cot2 A)-(sin2 A - sin4 A)

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