A) \[cos\,60{}^\circ \]
B) \[sin\text{ }60{}^\circ \]
C) \[tan\,60{}^\circ \]
D) \[cot\text{ }60{}^\circ \]
Correct Answer: C
Solution :
Given, \[\frac{2\tan \,30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\] \[=\frac{2\times \frac{1}{\sqrt{3}}}{1-{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}}\] \[\left[ \because \,\,\,\tan 30{}^\circ =\frac{1}{\sqrt{3}} \right]\] \[\Rightarrow \,\,\,\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}=\frac{2}{\sqrt{3}}\left[ \frac{1}{3-1} \right]\times 3\] \[=\frac{1}{\sqrt{3}}\times 3=\sqrt{3}=\tan \,60{}^\circ \]
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