Question

If $f\left(x\right)=\cos \left[\pi \right]x+\cos \left[\pi x\right],$ where $\left[y\right]$ is the greatest inetger function of $y$ then $f\left(\frac{\pi }{2}\right)$ is equal to

• A. $\cos 3$
• B. $0$
• C. $\cos 4$
• D. None of these

Answer 1

The correct option is C $\cos 4$

$f\left(\frac{\pi }{2}\right)$

$=\cos \left[\pi \right]\left(\frac{\pi }{2}\right)+\cos \left[\frac{{\pi }^2}{2}\right]$

$=\cos \left[3.14\right]\frac{\pi }{2}+\cos \left[4.93\right]$

$=\cos \left(\frac{3\pi }{2}\right)+\cos \left(4\right)$

$=\cos \left(4\right)$.

Hence the answer is $\cos \left(4\right)$.