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Question: If tan<sup>–1</sup> x + 2 cot<sup>–1</sup> x = \(\frac { 2 \pi } { 3 }\), then x =...

If tan–1 x + 2 cot–1 x = 2π3\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–1 x + cot–1 x + cot–1 x = 2p/3

Ž cot–1 x =2p/3 – p/2 = p/6

Ž