# $\sin(3x) = \sin(x)$

I recognize I'm intended to do $\sin(3x) - \sin x = 0$ yet past that I'm stuck. I attempted increasing $\sin(3x)$ yet that really did not aid.

• I desire the value of $x$ in the interval $[0, 2\pi)$
0
2019-05-13 03:33:24
Source Share

You can make use of the reality that $\sin x=\sin y$ if and also just if either $x-y$ is an also integer times $\pi$ or $x+y$ is a weird integer times $\pi$.

0
2019-05-17 14:56:29
Source

We have $\sin{3x} = 3\sin{x} - 4\sin^{3}{x}$ which claims that we need to address the formula $$3\sin{x} - 4\sin^{3}{x} - \sin{x}=0$$, that is $2 \sin{x} - 4\sin^{3}{x}=0$. Take $y = \sin{x}$ therefore you have $$2y-4y^{3}=0 \Longrightarrow 2y(1-2y^{2})=0$$ and afterwards see what takes place. I wish this aids you out.

Or you can also attempt this $$\sin{3x} - \sin{x} = 2 \cos\Bigl(\frac{3x+x}{2}\Bigr) \cdot \sin\Bigl(\frac{3x-x}{2}\Bigr) = 2\cos{2x} \cdot \sin{x}$$

0
2019-05-17 14:48:22
Source