# Write the acute angle θ satisfying 3–√ sin θ=cos θ.

Question:

Write the acute angle $\theta$ satisfying $\sqrt{3} \sin \theta=\cos \theta$.

Solution:

We have: $\sqrt{3} \sin \theta=\cos \theta$

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

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

$\Rightarrow \tan \theta=\tan 30^{\circ}$

$\Rightarrow \theta=30^{\circ}$

Hence the acute angle is