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:

sinA sin (A+B) = sinA [sin cosB + cosA sinB]

= sin2A cosB + (sinB)×SinA cosA

= sin2A cosA +1/2× sinA cosA (sinB)

= sin2A cosB + 1/2 (sinA) (sinB)