Prove the following identity:

(1 + tan A)² + (1 - tan A)² = 2 sec² A

Solving L.H.S. of the equation :

⇒ (1 + tan A)² + (1 - tan A)²

⇒ 1 + tan²A + 2 tan A + 1 + tan² A - 2 tan A

⇒ 2 + 2 tan²A

⇒ 2(1 + tan²A)

By formula,

1 + tan²A = sec² A

⇒ 2sec² A

Since, L.H.S. = R.H.S.

Hence, proved that (1 + tan A)² + (1 - tan A)² = 2 sec² A.