The period of `sin""(pi[x])/12+cos""(pi[x])/4+tan""(pi[x])/3`, where [x] represents the greatest integer less than or equal to x is

if f(x)=(sin(4 pi[x]))/(1+[x]^(2)), where [x] is the greatest integer less than or equal to x ,

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

The period of sin((pi x)/(2))+cos((pi x)/(3)) is

If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x where [x] denotes the greatest integer less than or equal to x then

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

The function f(x) = 3^(sin^(2)pi + sin^(4) pi x + x-[x]) where [x] denotes the greatest interger less than or equal to x, is

The value of int_(-pi//2)^(pi//2)(dx)/([x] + [ sin x] +4) , where [t] denotes the greatest integer than or equal to t , is

Number of points of discontinuity of the function f(x)=[(6x)/(pi)]cos[(3x)/(pi)] where [y] denotes the greatest integer function less than or equal to y) in the interval [0,(pi)/(2)] is

The equation sin x=[1+sin x]+[1-cos x) has (where [x] is the greatest integer less than or equal to 'x')

The range of f(x)=[sin x+[cos x+[tan x+[sec x]]]],x in(0,(pi)/(4)), where [.] denotes the greatest integer function less than or equal to x is