Question

If ${\displaystyle \sqrt{3}\sin \theta =\cos \theta \text{and}\theta }$ is an acute angle, find the value of θ .

Answer 1

We have ,

 ${\displaystyle \sqrt{3}\sin \theta =\cos \theta }$

⇒ ${\displaystyle \frac{\sin \theta }{\cos \theta }=\frac{1}{\sqrt{3}}}$

⇒ ${\displaystyle \tan \theta =\frac{1}{\sqrt{3}}}$

⇒  ${\displaystyle \tan \theta =\tan 30°}$

∴ ${\displaystyle \theta = 30°}$