Question

Prove the identity tan^2(x) - sin^2(x) = tan^2(x) sin^2(x)

Answer 1

Hi ,

LHS = tan²x - sin²x

= sin²x / cos²x - sin²x / 1

= sin²x [ 1 / cos²x - 1 / 1 ]

= sin²x [ ( 1 - cos²x ) / cos²x ]

= ( sin²x / cos²x ) ( 1 - cos²x )

= tan²x sin²x

= RHS

I hope this helps you.

:)