Find the general solutions of each of the following equation.
$\sqrt{3} cos x - sin x = 1$

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Solution

$\sqrt{3} cos x - sin x = 1 \Rightarrow \frac{\sqrt{3}}{2} cos x - sin x . \frac{1}{2} = \frac{1}{2} \Rightarrow sin \frac{π}{3} cos x - cos \frac{π}{3} sin x = \frac{1}{2} \Rightarrow sin (\frac{π}{3} - x) = sin (\frac{π}{6}) ∴ x = 2 n π + \frac{π}{6} o r x = 2 n π + \frac{3 π}{2}$

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