Question

If $f\left(x\right)=sin\left[{\pi }^2\right]x+sin[-\pi {]}^{2}x$, where [x] denotes teh greatest integer less than or equal to x, then,

• A. $f\left(\frac{\pi }{2}\right)=1$
• B. $f\left(\pi \right)=2$
• C. $f\left(\frac{\pi }{4}\right)=-1$
• D. None of these

Answer 1

The correct option is A

$f\left(\frac{\pi }{2}\right)=1$

$f\left(x\right)sin\left[{\pi }^2\right]x+sin[-\pi {]}^{2}x\Rightarrow f(x)=sin[9.8]x+sin[-9.8]x\Rightarrow f(x)=sin9x-sin10xf\left(\frac{\pi }{2}\right)=sin9\times \frac{\pi }{2}-sin10\times \frac{\pi }{2}\Rightarrow f\left(\frac{\pi }{2}\right)=1-0=1$