How to solve this trigonometric equation: $\sin3x+\sin5x=\sin6x+\sin2x$ Solve for $x$ $$\sin3x+\sin5x=\sin6x+\sin2x$$ I tried: $$\sin3x+\sin(2x+3x)=\sin(2*3x)+\sin2x$$ $$\sin3x+\sin2x*\cos3x+\cos2x*\sin3x=2\sin3x*\cos3x+\sin2x$$ ... After that i have no idea what to do. If i try with $\sin(x+2x)$ or something similar, it becomes even more scarry.

**Hint:** use the formula $$\sin x+\sin y = 2\sin {x+y\over 2}\cdot \cos{x-y\over 2}$$ and $$\cos x-\cos y = -2\sin {x+y\over 2}\cdot \sin{x-y\over 2}$$