1.

Prove that sin (A + B) sin (A – B) = cos2 B – cos2 A

Answer»

LHS = sin (A + B) sin (A – B) 

= (sin A cos B + cos A sin B) (sin A cos B – cos A sin B) 

= sin2 A cos2 B – cos2 A sin2

= (1 – cos2 A) cos2 B – cos2 A (1 – cos2 B) 

= cos2 B – cos2 A cos2 B – cos2 A + cos2 A cos2

= cos2 B – cos2 A = RHS



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