Question

Prove that (Sin A + Cos A) ² + (Cos A + Sec A) ² = 7 + Tan² A + Cot² A

Answer 1

Answer:

Given:

(sin A + cosec A)^2 + (cos A + sec A)^2

To Find:

7 + tan^2A + cot^2A

Proof:

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

sin^2A + cosec^2A + 2 sinA. cosec A + cos^2A + sec^2A + 2 cosA . secA

here sin^2A+cos^2A =1

1 + 2 + 2 + cosec^2A + sec^2A

here cosec^2A = 1+cot^2A  ,  sec^2A =  1+tan^2A

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

7 + cot^2A + tan^2A