Question

If $\cos \theta +\sqrt{3}\sin \theta =2$, then the value of $\theta$ is equal to

Answer 1

$1\times \cos \theta +\sqrt{3}\sin \theta =2$
$\Rightarrow (\frac{1}{2}\cos \theta +\frac{\sqrt{3}}{2}\sin \theta )=1$
$\Rightarrow \sin {30}^0\cos \theta +\cos {30}^0\sin \theta =1$
$\Rightarrow \sin (\theta +{30}^0)=\sin {90}^0$
$\Rightarrow \theta +{30}^0={90}^{0}or\theta ={60}^0$