Question

`(1+tan^2A)/(1+cot^2A)` = ______.

Options

• sec² A

• −1

• cot² A

• tan² A

Answer 1

`(1+tan^2A)/(1+cot^2A)` = tan² A.

Explanation:

`(1+tan^2A)/(1+cot^2A) = (1+(sin^2A)/cos^2A)/(1+(cos^2A)/(sin^2A))`

= `((cos^2A  +  sin^2A)/cos^2A)/((sin^2A  +  cos^2A)/sin^2A)`

= `(1/cos^2A)/(1/sin^2A)`

= `(sin^2A)/cos^2A`

= `tan^2A`

Hence, alternative tan² A is correct.