Select the correct identity from the following options.

$1 + tan^2 A = sec^2 A$

Lets solve one by one for each option,

Option 1:-

We know that  ,

sin²θ + cos²θ = 1

So ,  sin²θ = 1 -  cos²θ

Option 1 not followed.

option 2:-

sin²θ + cos²θ = 1

cos²θ = 1 - sin²θ

Option 2 not followed.

Option 3 :-

sec²θ - tan²θ = 1

sec²θ  = 1 + tan²θ

According to option 3

sec²A  = 1 + tan²A

so option 3 is followed.

Option 4 :-

sec²θ - tan²θ = 1

tan²θ  = sec²θ -1

Option 4 is not followed. 

Ans :- Option 3

sec²A  = 1 + tan²A