Question

SIN (A+B)SIN(A-B) = SIN^2 A - SIN^2 B PROVE STATEMENT please answer fast

Answer 1

As we do not know trigonometry we take sin as a multiplier So sin (a+b) = sin a + sin b And sin (a-b) = sin a – sin b Multiply them to get Sin (a+b) sin (a-b) = (sin a + sin b) (sin a - sin b) = sin ^2 a – sin ^2 b however above is wrong but the ans is right now to the correct approach Sin (a+b) sin (a-b) = (sin a cos b + cos a sin b)(sin a cos b – cos a sin b) = sin ^2 a cos^2b – cos^2 a sin ^2b = sin ^2 a(1- sin ^2 b) – cos^2 a sin ^2 b = sin ^2 a – sin ^2 a sin ^2 b – cos^2 a sin^2 b = sin ^2 a – sin ^2 b(sin ^2 a + cos^2 a) = sin ^2 a – sin ^2 b