A) \[2\sqrt{3}a\]
B) \[\sqrt{3}a\]
C) \[2\sqrt{3}{{a}^{2}}\]
D) None of these
Correct Answer: C
Solution :
Given equation is \[{{\tan }^{-1}}\frac{a+x}{a}+{{\tan }^{-1}}\frac{a-x}{a}=\frac{\pi }{6}\] \[\Rightarrow \,{{\tan }^{-1\,}}\left( \frac{\frac{a+x}{a}+\frac{a-x}{a}}{1-\frac{a+x}{a}.\,\frac{a-x}{a}} \right)=\frac{\pi }{6}\] \[\Rightarrow \,\,\frac{2{{a}^{2}}}{{{x}^{2}}}=\tan \frac{\pi }{6}=\frac{1}{\sqrt{3}}\,\,\Rightarrow \,\,{{x}^{2}}=2\sqrt{3}{{a}^{2}}\].
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