Question

Prove the following trigonometric identities.

`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`

Answer 1

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

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

`= tan^2 A`