Question

sin2x+sinx=0

Answer 1

\[\sin(2x) + \sin(x) \]\[= 2\sin\left(\frac{2x + x}{2}\right)\cos\left(\frac{2x - x}{2}\right)\]\[= 2 \sin\left(\frac{3x}{2}\right)\cos\left(\frac{x}{2}\right)=0\]\[\therefore \sin\left(\frac{3x}{2}\right) =0~~\text{or}~~\cos\left(\dfrac{x}{2}\right)=0\]