Question

Prove the following identity :-
(1 - tan A)^2 + (1 + tan A)^2 = 2 sec^2 A​

Answer 1

Answer:

2sec^2A

Step-by-step explanation:

firstly apply the identity (a-b)^2=a^2-2ab+b^2 and

(a+b)^2=a^2+2ab+b^2

so,

equation reduce to

=> (1+tan^2A-2tanA)+(1+tan^2A+2tanA)

=> (1+1+tan^2A+tan^2A+2tanA-2tanA)

=> (2+2tan^A)

now taking common 2

=> 2 (1+tan^2A)

here apply the identity 1+tan^2A=sec^2A

=> 2(sec^2A)