prove that:

(sinA + cosecA)^2 + (cosA + secA)^2 = 7 + tan^2A + cot^2A

Asked by Vru23 | 28th Jul, 2020, 08:20: PM

Expert Answer:

To prove:- (sinA + cosecA)2 + (cosA + secA)2 = 7 + tan2A + cot2A
LHS = (sinA + cosecA)2 + (cosA + secA)2 
= sin2A + cosec2A + 2 sinA cosecA + cos2A + sec2A + 2 cosA secA
= sin2A + cos2A + 2 + cosec2A + sec2A + 2
= 1 + 4 + cosec2A + sec2A
= 5 + 1 + cot2A + 1 + tan2A
= 7 + cot2A + tan2A
Hence proved.

Answered by Renu Varma | 29th Jul, 2020, 10:53: AM