Question

Prove that (1-tan A) 2 + (1+tan A) 2 = 2sec 2 A

Answer 1

Hi

we must show that:

(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

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Step-by-step explanation: