A) \[\frac{1}{\sqrt{3}}\]
B) \[\sqrt{3}\]
C) \[-\frac{1}{\sqrt{3}}\]
D) \[-\sqrt{3}\]
Correct Answer: B
Solution :
We know that \[\tan \,({{20}^{o}}+{{40}^{o}})=\frac{\tan \,{{20}^{o}}+\tan \,{{40}^{o}}}{1-\tan \,{{20}^{o}}\,\tan \,{{40}^{o}}}\] \[\Rightarrow \,\,\,\sqrt{3}=\frac{\tan \,{{20}^{o}}+\tan \,{{40}^{o}}}{1-\tan \,{{20}^{o}}\,\tan \,{{40}^{o}}}\] \[\Rightarrow \,\,\sqrt{3}-\sqrt{3}\,\tan \,{{20}^{o}}\,\tan \,{{40}^{o}}=\tan \,{{20}^{o}}+\tan \,{{40}^{o}}\] \[\Rightarrow \,\,\tan \,{{20}^{o}}+\tan \,{{40}^{o}}+\sqrt{3}\,\tan \,{{20}^{o}}\,\tan \,{{40}^{o}}=\sqrt{3}.\]
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