If f(x) = cos
Question:

If f(x) = cos [π2]x + cos [−π2x, 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 [−π2x

Thus, $f(\pi)=\cos \left[\pi^{2}\right] \pi+\cos \left[-\pi^{2}\right] \pi$

$\Rightarrow f(\pi)=\cos [9.8] \pi+\cos [-9.8] \pi$

$\Rightarrow f(\pi)=\cos 10 \pi+\cos 9 \pi$

$\Rightarrow f(\pi)=1+(-1)=0$

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