Find the sum of the integral values of `a` where `a in[20,100)` for which `[cot x]^(2)+cot x-a=0` has real roots? (where [ ] denotes greatest integer function)

The number of integral values of a , a in (6,100) for which the equation [tan x]^(2)+tanx-a=0 has real roots, where [.] denotes greatest integer function is ___________

If f(x)=[2x], where [.] denotes the greatest integer function,then

Sove [cot^(-1) x] + [cos^(-1) x] =0 , where [.] denotes the greatest integer function

the value of int_(0)^([x]) dx (where , [.] denotes the greatest integer function)

f(x)=1+[cos x]x, in 0<=x<=(x)/(2) (where [.] denotes greatest integer function)

The function,f(x)=[|x|]-|[x]| where [] denotes greatest integer function:

The equation x^(2)-2=[sin x], where [.] denotes the greatest integer function,has

The value of int_(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] denotes the greatest integer function)

If [log_2 (x/[[x]))]>=0 . where [.] denotes the greatest integer function, then :

The value of lim_(x rarr0)[(sin x)/(x)] is (where [.] denotes greatest integer function)