For the function $f\left(x\right)=\mathrm{s}\mathrm{i}\mathrm{n}\left(\pi \left[x\right]\right)\times \mathrm{c}\mathrm{o}{\mathrm{s}}^{-1}\left(\left[x\right]\right)$, choose the correct option.

(where $\left[.\right]$ represents the greatest integer function)

• A

  Domain of $f\left(x\right)\in \left[-\mathrm{1,1}\right]$
• B

  Range of $f\left(x\right)$ contains exactly two elements
• C

  $f\left(x\right)$ is an identity function
• Correct answer
  D

  $f\left(x\right)$ is a constant function

Hence, the correct answer is option: 'D'.