A) \[\sqrt{12}\]
B) \[\frac{1}{\sqrt{3}}\]
C) 1
D) \[\frac{\sqrt{3}}{2}\]
E) \[\sqrt{3}\]
Correct Answer: E
Solution :
We know that, \[tan\text{(}20{}^\circ +40{}^\circ )=\frac{\tan 20{}^\circ +\tan 40{}^\circ }{1-\tan 20{}^\circ \tan 40{}^\circ }\] \[\Rightarrow \] \[\sqrt{3}=\frac{\tan 20{}^\circ +\tan 40{}^\circ }{1-\tan 20{}^\circ \tan 40{}^\circ }\] \[\Rightarrow \] \[\sqrt{3}-\sqrt{3}\tan 20{}^\circ \tan 40{}^\circ \] \[=\tan 20{}^\circ +\tan 40{}^\circ \] \[\Rightarrow \] \[\tan 20{}^\circ +\tan 40{}^\circ +\sqrt{3}\tan 20{}^\circ \tan 40{}^\circ \] \[=\sqrt{3}\]
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