A) \[\sqrt{2}\]
B) 3
C) \[\sqrt{3}\]
D) \[\frac{\sqrt{3}-1}{\sqrt{3}+1}\]
Correct Answer: C
Solution :
The given equation may be written as \[{{\tan }^{-1}}x+{{\cot }^{-1}}x+{{\cot }^{-1}}x=\frac{2\pi }{3}\] Þ \[{{\cot }^{-1}}x=\frac{2\pi }{3}-\frac{\pi }{2}\] = \[\frac{\pi }{6}\] Þ \[x=\sqrt{3}\].
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