Question

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'B
here, ( ' )=square=power2
I know (B) is the answer but I want detailed solution,so please explain the answer properly and provide elaborated solution.

Thank you​​​

Answer 1

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