Question

sin 3A + sin 2A - sin A = 4 sinA cosA/2 cos 3A/2​

Answer 1

Answer:

$\sin(3x) - \sin(x) + \sin(2x) \\ = 2 \sin( \frac{3x - x}{2} ) cos( \frac{ 3x + x } {2} ) + 2 \sin(x) \cos(x) \\ = 2 \sin(x) \cos(2x) + 2 \sin(x) \cos(x) \\ = 2 \sin(x) ( \cos(2x) + \cos(x) ) \\ = 2 \sin(x) (2 \cos( \frac{x + 2x}{2} ) \cos( \frac{2x - x}{2} ) \\ = 4 \sin(x) \cos( \frac{x}{2} ) \cos( \frac{3x}{2} )$