$sin 6 x = sin 4 x - sin 2 x$ Find the value of $x$ .

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Solution

$(sin 6 x + sin 2 x) - sin 4 x = 0$
or $2 sin 4 x cos 2 x - sin 4 x = 0$
$∴ sin 4 x = 0$ or $cos 2 x = \frac{1}{2} = cos \frac{π}{3}$
$∴ 4 x = n π$ or $2 x = 2 n π \pm \frac{π}{3}$
$∴ x = \frac{n π}{4}$ or $x = n π \pm \frac{π}{6}$ .

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