Find the general solution for the equation cos 7x − cos 4x + cos x = 0


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Question Number 157324 by ZiYangLee last updated on 22/Oct/21

$Find the general solution for the equation$ $\cos 7 x - \cos 4 x + \cos x = 0$
Commented by cortano last updated on 22/Oct/21

$\cos 7 x + \cos x - \cos 4 x = 0$ $2 \cos 4 x \cos 3 x - \cos 4 x = 0$ $\cos 4 x (2 \cos 3 x - 1) = 0$ ${\begin{cases} \cos 4 x = 0 \\ \cos 3 x = \frac{1}{2} \end{cases}$
	Answered by gsk2684 last updated on 22/Oct/21

	$\cos 7 x + \cos x - \cos 4 x = 0$ $2 \cos (\frac{7 x + x}{2}) \cos (\frac{7 x - x}{2}) - \cos 4 x = 0$ $\cos 4 x (2 \cos 3 x - 1) = 0$ $\cos 4 x = 0 o r \cos 3 x = \frac{1}{2}$ $4 x = (2 n + 1) \frac{π}{2} o r 3 x = 2 n π \pm \frac{π}{3} w h e r e n \in I$ $x = (2 n + 1) \frac{π}{8} o r x = \frac{2 n π}{3} \pm \frac{π}{9} w h e r e n \in I$
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