Question

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

Answer 1

Answer:

LHS = ( sin A + cosec A )² + ( cos A + sec A )²

sin² A + cosec² A + 2 sin A cosec A + cos²A + sec² A + 2 cos A

sec A

= 1 + 2 + 2 + cosec² A + sec² A

= 1 + 2 + 2 + cot ² A + 1 + 1 + tan² A

= 7 + cot² A + tan² A = RHS

Hence proved