Question
Write the acute angle $\theta$ satisfying $\sqrt{3}\sin\theta=\cos\theta.$
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Answer
We have: $\sqrt{3}\sin\theta=\cos\theta$
$\Rightarrow\sqrt{3}\sin\theta=\cos\theta$
$\Rightarrow\frac{\sin\theta}{\cos\theta}=\frac{1}{\sqrt{3}}$
$\Rightarrow\tan\theta=\tan30^\circ$
$\Rightarrow\theta=30^\circ$
Hence the acute angle is 30°
$\Rightarrow\sqrt{3}\sin\theta=\cos\theta$
$\Rightarrow\frac{\sin\theta}{\cos\theta}=\frac{1}{\sqrt{3}}$
$\Rightarrow\tan\theta=\tan30^\circ$
$\Rightarrow\theta=30^\circ$
Hence the acute angle is 30°
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