Question

prove that sina+cosa/sina-cosa+sina-cosa/sina+cosa=1/sin^2a-cos^2a=2/1-2 cos^2a=2sec^2a/tan^2a-1

Answer 1

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Answer 2

Answer:3 answers · Mathematics

Best Answer

LHS=

= (sinA+cosA)^2 + (sinA-cosA)^2 / (sin^2A - cos^A)

= 2 / ( (1-cos^2A) - cos^2A) ---------------> sin^2A + cos^2A = 1

Divide Numerator (Nr) and Denominator (Dr) by 'cos^2A'

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

Nr ==> 2sec^2A

Dr => (1/cos^2A) - (2cos^2A/cos^2A)

But sec^2A = tan^2A + 1

Hence Dr ==> tan^2A + 1 - 2

Dr = tan^2A -1

Hence LHS = Nr/Dr = RHS