Q. sinA.sin(A + B) is equal to(A) cos'A.cosB + sinA.sin'B(B) sin'A. 1/

1.	Q. sinA.sin(A + B) is equal to(A) cos'A.cosB + sinA.sin'B(B) sin'A. 1/2cosB + COS2A.sinB(C) sin'A.cosB + 1/2sin2A.sinB(D) sin'A.sinB + cosA.cos'Bhere, ( ' )=square=power2I know (B) is the answer but I want detailed solution,so please explain the answer properly and provide elaborated solution.Thank you
Answer» ANSWER: $\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b)$ $\sin(a) \sin(a + b) = \sin(a) (\sin(a) \cos(b) + \cos(a) \sin(b) )$ after MULTIPLY $= { \sin(a) }^{2} \cos(b) + \cos(a) \sin(a) \sin(b)$ divide and multiply by 2 $= { \sin(a) }^{2} \cos(b) + \frac{1}{2} \sin(2a) \sin(b)$ therefore OPTION C is RIGHT