Question

( sin A + cosec A)^2 +( cos A + sec A)^2 =7 +tan^2 A + cot^ 2

Answer 1

solving LHS,

= (sinA + cosecA)^2 + (cosA + secA)^2

= (sin^2A + cosec^2A +2sinAcosecA) + (cos^2A + sec^2A + 2cosAsecA)

= sin^2A + cosec^2A + 2 + cos^2A + sec^2A + 2

=4 + 1 + cosec^2A + sec^2A

now, I we know cosec^2A = cot^2A +1
and sec^2A = tan^2A + 1

therefore,

= 5 + cot^2A + 1 + tan^2A + 1

= 7 + cot^2A + tan^2A

LHS = RHS

hence proved.