Question

prove that tan square A minus tan square B is equals to sin square A minus sin square b by cos square a into to cos square B

Answer 1

tan²A - tan²B = sin²A - sin²B ÷ cos² A * cos²B

LHS.,

tan²A - tan²B

⇒ sin²A/cos²A - sin²B/cos²B

⇒ cos²B.sin²A - cos²A.sin²B / cos²A.cos²B

⇒ (1-sin²B).sin²A - (1-sin²A).sin²B / cos²A.cos²B

⇒ sin²A - sin²A.sin²B - sin²B + sin²A.sin²B / cos²A.cos²B

⇒ sin²A - sin²B / cos²A.cos²B

Answer 2

Plzz check the attachment for answer.. Hope it is help full