Question

prove that (1+tan a*tan b)^2+(tan a-tan b)^2) = sec^2 a*sec^2 b​

Answer 1

Answer:

Taking L.H.S. , we have

LHS = (1 + tan a tan b)2 + (tan a – tan b)2

= 1 + tan2a tan2b + 2 tan a tan b + tan2a + tan2b – 2 tan a tan b

= 1 + tan2a tan2b + tan2a + tan2b

= 1. (1 + tan2b) + tan2a (tan2b + 1)

= (1 + tan2b) + (1 + tan2a)

= sec2b sec2a

= sec2a sec2b

= RHS

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