यदि `tan^(-1) x + 2 cot^(-1) x = (2 pi)/3` है , तो x का मान होगा

Options

A. `sqrt3`
B. `sqrt3/2`
C. `sqrt3/4`
D. `1/sqrt3`

Answer

A

Explanation

`:' tan^(-1) x + 2 cot ^(-1) x = (2pi)/3`[दिया है ]
` rArr tan^(-1) x + 2 tan^(-1)(1/x) = (2pi)/3`
` [:' tan^(-1) x = cot^(-1) 1/x]`
` rArr tan^(-1) x + tan^(-1)((2/x)/(1-1/x^(2)))= (2pi)/3`
` rArr tan^(-1)((x^(3)+x)/(-1 - x^(2))) = (2pi)/3`
` rArr tan^(-1)(-x) = (2pi)/3`
` rArr x = sqrt3`