Question

prove the following identity
( Sin A + cosecA)^2 + Cos A + set A )^2 = 7 + tan^2 A + cos^2 A

Answer 1

(sinA+cosecA)^2 + (CosA+ SecA)^2
sin^2A + cosec^2A + 2 + Cos^2A + Sec^2A +2
since sin^2A + cos^2A =1 and cosec^2A = cot^2A + 1 and also sec^2A=tan^2A + 1
so,
1 + tan^2A + 1 + cot^2A + 1 + 4
7+ tan^2A + cot^2A= L.H.S


Proved