10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

If \[\sin \theta =\sqrt{3}\,\,\cos \theta ,\]\[0{}^\circ <\theta <90{}^\circ ,\]then \[\theta \]is equal to:

A) \[30{}^\circ \]

B) \[45{}^\circ \]

C) \[60{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: C

Solution :

[c]\[\sin \theta =\sqrt{3}\cos \theta \]

\[\Rightarrow \,\,\,\,\,\frac{\sin \theta }{\cos \theta }=\sqrt{3}\]

\[\Rightarrow \,\,\,\,\,\tan \theta =\sqrt{3}=\tan 60{}^\circ \]

\[\Rightarrow \,\,\,\,\,\theta =60{}^\circ \]