Question

(1-tanA)^2 + (1+tanA)^2 =2sec^2A

Answer 1

 

(1+tanA)²+(1-tanA)²=2 sec²A

we consider the first member:
(1+tanA)²+(1-tanA)²
we have that:
(1+tanA)²+(1-tanA)²;
= 1+tan²A+2tanA+1+tan²A-2tanA;
=2+2tan²A

being sen²A-tan²A=1 that is sec²A=1+tan²A;
so you have:
2+2tan²A;
=2(1+tan²A);
=2sec²A