Question

Range of $f\left(x\right)=\frac{\tan \left(\pi [x^2-x]\right)}{1+\sin \left(\cos x\right)}$ is where $\left[x\right]$ denotes the greatest integer function

• A. $(-\infty ,\infty )-[0,\tan 1]$
• B. $\left\{0\right\}$
• C. $(-\infty ,\infty )-[\tan 2,0)$
• D. $[\tan 2,\tan 1]$

Answer 1

The correct option is B

$\left\{0\right\}$

$f\left(x\right)=\frac{\tan \left(\pi [x^2-x]\right)}{1+\sin \left(\cos x\right)}$
Since $[x^2-x]$ is always an integer $\Rightarrow \tan \left(\pi [x^2-x]\right)=0$
$\Rightarrow f\left(x\right)=\frac{\tan \left(\pi [x^2-x]\right)}{1+\sin \left(\cos x\right)}=0$