Question

Find the range of

$f\left(x\right)=\frac{\tan \left(\pi \right[x^2-x\left]\right)}{1+\sin \left(\cos x\right)}$

• A. $\left\{0\right\}$
• B. $\{0,1\}$
• C. $\{-1,0,1\}$
• D. $\left\{\frac{\pi }{2}\right\}$

Answer 1

The correct option is A $\left\{0\right\}$

For all $x\in R$ numerator will take value $\tan n\pi$, where $n$ is any integer.
And we know $\tan n\pi =0$. Hence $f\left(x\right)=0\forall x\in R$