If `x in (0,pi/2)` satisfies the inequality `[tan x-sqrt3|+|4sin^2x-3|+|tan (tan^-1x)-pi/3] le 0,` then the value of `tan(cot^(- 1)((sqrt(2))/(30 x)cos((3x)/4))].` [Note : [.] denotes greatest integer function.]

If x in(0,(pi)/(2)) satisfies the inequality [tan x-sqrt(3)|+|4sin^(2)x-3|+|tan(tan^(-1)x)-(pi)/(3)]<=0 then the value of tan(cot^(-1)((sqrt(2))/(30x)cos((3x)/(4)))]*[ Note : [.] denotes greatest integer function.]

The value of int_(0)^((pi)/(3))[sqrt(3)tan x]dx( where [.] denotes the greatest integer function.) is:

If x satisfies the inequality (tan^-1x)^2+3(tan^-1x)-4gt0 , then the complete set of values of x is

Let f(x)=sin(tan^(-1)x). Then [f(-sqrt(3))] where [*] denotes the greatest integer function,is

If all values of x in (a, b) satisfy the inequality tan x tan 3x lt -1, x in (0, (pi)/(2)) , then the maximum value of (b-a) is :

If [2cos x]+[sin x]=-3, then the range of the function,f(x)=sin x+sqrt(3)cos x in [0,2 pi] (where [1 denotes greatest integer function)

If tan^(-1)(2x)+tan^(-1)(3x)=(pi)/(4) , then find the value of x.

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

If (x)=[tan^(-1)(tan x):x (pi)/(4) then jump of discontinuity is (where [.] denotes greatest integer function)