1. ## Trigonometric equation

$$\sin{x}+\sin{2x}+\sin{3x}+\sin{4x}=0$$

I'm having a lot of trouble solving this... Didn't really get anywhere so nothing to show. I assume the solution has something to do with the fact that
4x + x = 5x, and 2x + 3x = 5x, but I have absolutely no idea

2. ## Re: Trigonometric equation

Nevermind I figured it out.
$$\sin(2x-x)+\sin(2x+x)+\sin(3x-x)+\sin(3x+x)=0$$
$$2\sin{2x}\cos{x}+2\sin{3x}\cos{x}=0$$
$$\cos{x}(\sin{2x}+\sin{3x})=0$$

And it's simple from there.

Sorry.