The sum of roots of the equation `cos^(-1)(cosx)=[x],[dot]` denotes the greatest integer function, is (a)`2pi+3` (b) `pi+3` (c) `pi-3` (d) 2`pi-3`

Prove that int_(-pi/2)^(2pi)[cot^(-1)x]dx ,where [dot] denotes the greatest integer function.

The period of the function f(x)=(6x+7)+cospix-6x , where [dot] denotes the greatest integer function is: 3 (b) 2 pi (c) 2 (d) none of these

The range of sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [.] denotes the greatest integer function, is {pi/2,pi} (b) {pi} (c) {pi/2} (d) none of these

Draw the graph of y = cos x, x in [0, 2pi], where [*] denotes the greatest integer function.

The number of solutions of [sinx+cosx]=3+[-sinx]+[-cosx](w h e r e[] denotes the greatest integer function), x in [0,2pi] , is 0 (b) 4 (c) infinite (d) 1

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is

The value of int_(e)^(pi^(2))[log_(pi)x]d(log_(e)x) (where [.] denotes greatest integer function) is

The number of solutions of the equation cos^(2)((pi)/(3)cos x - (8pi)/(3))=1 in the interval [0,10pi] is

Find the number of solution of [cosx]+|sinx|=1, x inpilt=xlt=3pi (where [ ] denotes the greatest integer function).

int_0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot] denotes the greatest integer function is equal to -npi (b) -(n+1)pi 2npi (d) -(2n+1)pi