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Prove that sin 3A + sin 2A - sin A = 4 sin A cos(A/2) cos(3A/2). Which statement is correct?

1. It is a valid identity
2. It is false; RHS should have sin instead of cos
3. It holds only for A = 0
4. RHS should be 2 sin A cos(A/2) cos(3A/2)

Correct answer: It is a valid identity

Solution

Combining sin 3A - sin A = 2 cos2A sinA with sin2A = 2 sinA cosA, factoring 2 sinA and using cos2A + cosA = 2 cos(3A/2)cos(A/2) gives the RHS.

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