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Question: If \(\tan ^ { - 1 } x + 2 \cot ^ { - 1 } x = \frac { 2 \pi } { 3 }\) then x =...

If tan⁡−1x+2cot⁡−1x=2π3\tan ^ { - 1 } x + 2 \cot ^ { - 1 } x = \frac { 2 \pi } { 3 } then x =

A

2\sqrt { 2 }

B

3

C

3\sqrt { 3 }

D

3−13+1\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }

Answer

3\sqrt { 3 }

Explanation

Solution

The given equation may be written as

tan⁡−1x+cot⁡−1x+cot⁡−1x=2π3\tan ^ { - 1 } x + \cot ^ { - 1 } x + \cot ^ { - 1 } x = \frac { 2 \pi } { 3 }

⇒ x=3x = \sqrt { 3 }.