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Higher Order Derivatives

Solve the fol...

Question

Solve the following equation:
$cos 2 x cos x = sin 7 x sin 6 x + 5 cos \frac{π}{2}$

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Solution

$cos 2 x cos x = sin 7 x sin 6 x + 5 cos \frac{π}{2}$
$cos (3 x) + cos x = cos x - cos 13 x$
$cos 3 x + cos 13 x = 0$
$2 cos 8 x cos 5 x = 0$
Either, $cos 8 x = 0, 8 x = (2 n + 1) \frac{π}{2}, x = (2 n + 1) \frac{π}{16} .$
or, $cos 5 x = 0, 5 x = (2 n + 1) \frac{π}{2}, x = (2 n + 1) \frac{π}{10} .$

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