f(x) Transforms to [f([x])]

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite