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Circular Measurement of Angle

Solve the fol...

Question

Solve the following equation:
$cos 3 x = \frac{\sqrt{3}}{2} cos x - \frac{1}{2} sin x .$

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Solution

$cos 3 x = \frac{\sqrt{3}}{2} cos x - \frac{1}{2} sin x .$
$cos 3 x = cos (30 ° + x)$
$3 x = 2 n π \pm (30 ° + x)$
Taking the $s i g n$ , we get $x = n \frac{π}{2} - \frac{15 °}{2}, a n d x = n x + 15 ° .$

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