Question

Solve the following equation:
$\sqrt{3}\cos \theta +\sin \theta =1$

Answer 1

$\frac{\sqrt{3}}{2}\cos \theta +\frac{1}{2}\sin \theta =\frac{1}{2}$

$\cos 30\cos \theta +\sin 30\sin \theta =\frac{1}{2}$

$\cos (30-\theta )=\frac{1}{2}=\cos {60}^o$

$\Rightarrow 30-\theta =60$

or $\theta -30={60}^o$

$\Rightarrow \theta =-{30}^o$ or $\theta ={90}^o$.