sec 2 A +cosec 2 A=13

Given
$ \sec^2 A + \cosec^2 A = 13 $ and $A$ is an acute angle.

Step 1: Use identities

We know,

$ \sec^2 A = 1 + \tan^2 A $
$ \cosec^2 A = 1 + \cot^2 A $

Substitute into the given equation:

$ (1+\tan^2 A) + (1+\cot^2 A) = 13 $

Step 2: Simplify

$ 2 + \tan^2 A + \cot^2 A = 13 $

$ \tan^2 A + \cot^2 A = 13 - 2 $

$ \tan^2 A + \cot^2 A = 11 $

✅ Final Answer: 11