Question

( sinA+ cosecA)^2+(cosA+secA)^2=5+sec^2A.cosec^2A

Prove the above identity.

Answer 1

You need to use ^ to denote exponents.
Without it, sec2A could be sec(2A)

(sin A + csc A)² + (cos A + sec A)²
= (sin A + 1/sin A)² + (cos A + 1/cos A)²
= sin²A + 2 + 1/sin²A + cos²A + 2 + 1/cos²A
= (sin²A + cos²A) + 4 + 1/sin²A + 1/cos²A
= 5 + (cos²A + sin²A) / (sin²A cos²A)
= 5 + 1 / (sin²A cos²A)
= 5 + (1/cos²A) (1/sin²A)
= 5 + sec²A cosec²A