Question

Prove the identity
tan²x - sin²x = tan²x sin²x

Answer 1

Answer:

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Refer the attachment...

Answer 2

TO PROVE

tan²x - sin²x = tan²x sin²x

SOLUTION

We know that tanx = sinx/cosx

LHS

= tan²x - sin²x

= sin²x/cos²x - sin²x

= [sin²x - cos²x sin²x ] / cos²x

= sin²x [ 1 - cos²x ] / cos²x

= sin²x × sin²x / cos²x

= tan²x sin²x

= RHS

HENCE PROVED ✓✓

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