Paragraph: Let f(x)= [π^2] x+ [-π^2] x where [.] is a greatest...

$f(x)=\sin \left[\pi^2\right] x+\cos \left[-\pi^2\right] x\because \quad \pi^2=(3 \cdot 14)^2$ Hence $\left[\pi^2\right]=9$ and \left[-\pi^2\right]=-10f(x)=\sin 9 x+\cos (-10 x)=\sin 9 x+\cos 10 xf\left(\frac{\pi}{2}\right)=\sin \frac{9 \pi}{2}+\cos \frac{10 \cdot \pi}{2}=\sin \left(4 \pi+\frac{\pi}{2}\right)+\cos 5 \pi=0