A) \[\frac{123}{25}\]
B) \[\frac{312}{25}\]
C) \[\frac{231}{25}\]
D) \[\frac{192}{25}\]
Correct Answer: B
Solution :
\[\frac{2\sin \theta \cos \theta }{{{\cos }^{2}}\theta -{{\sin }^{2}}\theta }=\frac{2\cdot \frac{\sin \theta }{\cos \theta }}{1-\frac{{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }}=\frac{2\,\,\tan \theta }{1-{{\tan }^{2}}\theta }\] \[=\frac{2\times \frac{12}{13}}{1-{{\left( \frac{12}{13} \right)}^{2}}}=\frac{\frac{24}{13}}{\frac{25}{169}}=\frac{24}{13}\times \frac{169}{25}=\frac{312}{25}\]
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