Question

1+tan2 A/1+Cot²A, then A is equal to
Sec2 A b) tan2A c) Cot²A d) tanA​

Answer 1

Answer:

Explanation:

:

Here, we will use, tan2A=2tanA1−tan2A

1+tanAtan(A2)=1+⎛⎝⎜2tan(A2)1−tan2(A2)⋅tan(A2)⎞⎠⎟

=1−tan2(A2)+2tan2(A2)1−tan2(A2)

=1+tan2(A2)1−tan2(A2)

=sec2(A2)cos2(A2)−sin2(A2)cos2(a2)

=sec2(A2)sec2(A2)cosA=secA

Now,  tanAcot(A2)−1=⎛⎝⎜2tan(A2)1−tan2(A2)⎞⎠⎟(1tan(a2))−1  

2−1+tan2(A2)1−tan2(A2)

=1+tan2(A2)1−tan2(A2)

=sec2(A2)cos2(A2)−sin2(A2)cos2(a2)

=sec2(A2)sec2(A2)cosA=secA