1+tan2A/1+cot2A =(A) sec2 A (B) -1 (C) cot2A (D) tan2A

Dear Student

option (D) is correct.

Justification:
We know that,
tan^2 A =1/cot^2 A
Now, substitute this in the given problem, we get

1+tan^2 A/1+cot^2 A
= (1+1/cot^2 A)/1+cot^2 A
= (cot^2 A+1/cot^2 A)×(1/1+cot^2 A) = 1/cot^2 A = tan^2 A
So, 1+tan^2 A/1+cot^2 A = tan^2 A
Thanks