Find the number of solution for the equation $sin 2 x + sin 4 x = 2 sin 3 x$ between the interval $0 \leq x \leq π$

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Solution

Given, $sin 2 x + sin 4 x = 2 sin 3 x$
$\Rightarrow 2 sin 3 x cos x = 2 sin 3 x$
$\Rightarrow sin 3 x cos x - sin 3 x = 0$
$\Rightarrow sin 3 x (cos x - 1) = 0$
$\Rightarrow sin 3 x = 0$ or $cos x = 0$
$\Rightarrow x = \frac{n π}{3}$ or $x = 2 n π$

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