A) \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]
B) \[{{\tan }^{-1}}\left( 3 \right)\]
C) \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\]
D) \[{{\tan }^{-1}}(4)\]
Correct Answer: C
Solution :
We know that \[\tan \,2\alpha =\frac{2\tan \alpha }{1-{{\tan }^{2}}\alpha }=\frac{2\times \frac{1}{2}}{1-{{\left( \frac{1}{2} \right)}^{2}}}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\]. \[\therefore \,\,2\alpha ={{\tan }^{-1}}\left( \frac{4}{3} \right)\].
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