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

\[\frac{2\tan 30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\]is equal to: (NCERT EXEMPLAR)

A) \[\cos 60{}^\circ \]

B) \[\sin 60{}^\circ \]

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

D) \[\sin 30{}^\circ \]

Correct Answer: C

Solution :

[c]\[\frac{2\tan 30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\]

\[=\frac{2\times \frac{1}{\sqrt{3}}}{1-{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}}=\frac{2/\sqrt{3}}{1-1/3}\]

\[=\frac{2}{\sqrt{3}}\times \frac{3}{2}=\sqrt{3}=\tan 60{}^\circ \]