If `cos^-1 (x^2-1)/(x^2+1)+ tan^-1 (2x)/(x^2-1) = (2pi)/3`, then x equal to (A) `sqrt(3)` (B) `2+sqrt(3)` (C) `2-sqrt(3)` (D) `-sqrt(3)`

If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3 , then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If quad 3sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+2tan^(-1)((2x)/(1-x^(2)))=(pi)/(3) then x is equal to (A)(1)/(sqrt(3))(B)-(1)/(sqrt(3))(C)sqrt(3)(D)-(sqrt(3))/(4)

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)

If quad 3sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+2tan^(-2)((2x)/(1-x^(2)))=(pi)/(3),where|x|<1 then x is equal to (1)/(sqrt(3))(b)-(1)/(sqrt(3))(c)sqrt(3)(d)-(sqrt(3))/(4)

If |cos^(-1)((1-x^(2))/(1+x^(2)))|<(pi)/(3), then x in[-(1)/(3),(1)/(sqrt(3))] (b) x in[-(1)/(sqrt(3)),(1)/(sqrt(3))]x in[0,(1)/(sqrt(3))](d) none of these

If tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(6), then prove that x^(2)=2sqrt(3).

If 3tan^(-1)((1)/(2+sqrt(3)))-(tan^(-1)1)/(x)=(tan^(-1)1)/(3) then x is equal to 1(b)2(c)3(d)sqrt(2)

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

If x=5+2sqrt(6), then (x-1)/(sqrt(x)) is equal to a.sqrt(2) b.sqrt(3)c.2sqrt(2)d.2sqrt(3)