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

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 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 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 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 sin^(-1)x+cot^(-1)((1)/(2))=(pi)/(2), then x is 0b(1)/(sqrt(5))c*(2)/(sqrt(5))d*(sqrt(3))/(2)

If tan(cos^(-1)x)=sin(cot^(-1)1/2) then x is equal to- a.1/sqrt(5)b.2/sqrt(5)c.3/sqrt(5)d.sqrt(5)/3

If tan^(-1)(-sqrt(3))+cot^(-1)x=pi , then the value of x is :

If x tan45o cos60o=sin60o cot60o, then x is equal to 1(b)sqrt(3)(c)(1)/(2)(d)(1)/(sqrt(2))

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) cosalpha+cosbeta+cosgamma is equal to (A) (sqrt(2)-1)/2 (B) (sqrt(2)+1)/2 (C) (sqrt(2)+sqrt(3))/2 (D) ((sqrt(3)-sqrt(2))/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