Question:
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Solution:
f(x) = cos [π2]x + cos [−π2] x
Thus, $f(\pi)=\cos \left[\pi^{2}\right] \pi+\cos \left[-\pi^{2}\right] \pi$
$\Rightarrow f(\pi)=\cos [9.8] \pi+\cos [-9.8] \pi$
$\Rightarrow f(\pi)=\cos 10 \pi+\cos 9 \pi$
$\Rightarrow f(\pi)=1+(-1)=0$