Question

If, $f\left(x\right)=cos\left[{\pi }^2\right]x+cos[-{\pi }^2]x,$ where [x] stands for greatest integer function, then

• A. $f\left(\frac{\pi }{2}\right)=1$
• B. $f\left(\pi \right)=1$
• C. $f(-\pi )=0$
• D. $f\left(\frac{\pi }{4}\right)=2$

Answer 1

The correct option is C

$f(-\pi )=0$

$f\left(x\right)=cos\left[{\pi }^2\right]x+cos[-{\pi }^2]x$
f(x) = cos 9x + cos (-10)x
f(x) = cos 9x + cos 10 x
$\therefore f\left(\frac{\pi }{2}\right)=0-1=-1$
f $\left(\pi \right)$ = -1 + 1 = 0
f $(-\pi )$ = -1 + 1 = 0
$f\left(\frac{\pi }{4}\right)=\frac{1}{\sqrt{2}}+0=\frac{1}{\sqrt{2}}$