The number of integers in the range of function `f (x) = [ sin x] + [ sin x+ cos x]` is (where [.]= denotes greatet integer funcion)

Options

A. The number of points of discontinuity in `(0,pi)` is 3.
B. the number of points of discontinuity in `(0,pi)` is `4`
C. `f(x)` is discontinuous at `x=1,2,3`
D. `f(x)` is discontinuous at all integers.

Answer

B, C, D

Explanation

`f(x)=([x]+[-x]([sinx]+[-sinx])+x`
`{{:(x," , " x in I),(x," , "x in (npi)/2" , " n in I),(x+1," , " "otherwise"):}`
point of `D.C.x=1,2,3,(pi)/(2)`