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Expression Formation

Solve the fol...

Question

Solve the following equation:
$cos x + cos 4 x + cos 7 x = 0$

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Solution

$2 cos 4 x cos 3 x + cos 4 x = 0$
$cos 4 x (2 cos 3 x + 1) = 0$
So, $cos 4 x = 0, 4 x = (2 n + 1) \frac{π}{2}, x = (2 x + 1) \frac{π}{8} .$ and $cos 3 x = - \frac{1}{2}, 3 x = 2 n π \pm \frac{π}{3}, x = 2 n \frac{π}{3} \pm \frac{π}{9} .$

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