Question

Prove the following trigonometric identities:

sin²A cos²B - cos²Asin²B = sin²A - sin²B

Answer 1

To prove:  sin²A cos²B - cos²Asin²B = sin²A - sin²B

Proof: Take LHS, Use the identity sin²θ+cos²θ=1

sin²A cos²B - cos²A sin²B

= sin²A(1 – sin²B) – (1 – sin²A)sin²B 

sin²B – sin²B + sin²A sin²B

= sin²A – sin²B

= RHS Hence Proved