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Circular Measurement of Angle

Solve the fol...

Question

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

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Solution

$\frac{1}{\sqrt{2}} sin 3 x - \frac{1}{\sqrt{2}} cos 3 x = \frac{\sqrt{3}}{2}$
$sin (3 x - \frac{π}{4}) = \frac{\sqrt{3}}{2}$
$3 x - \frac{π}{4} = n π + {(- 1)}^{n} \frac{π}{3}$
$x = \frac{n π}{3} + {(- 1)}^{n} \frac{π}{9} + \frac{π}{12} .$

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