Question

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

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \sqrt{3}\sin \theta =\cos \theta \\ \Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{1}{\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{1}{\sqrt{3}} \\ \Rightarrow \tan \theta =\tan 30° \\ \therefore \theta =30° \end{gathered}$$