Question

For $x\in (0,\frac{\pi }{2}),\left[\sin x\right]-[-\sin x]=$ where $\left[x\right]$ is a greatest integer function.

• A. $-2\sin x$
• B. $1$
• C. $2\sin x$
• D. $2$

Answer 1

The correct option is B $1$

For $x\in (0,\frac{\pi }{2}),\sin x\in (0,1)$
$\Rightarrow \left[\sin x\right]=0\&[-\sin x]=-1\Rightarrow \left[\sin x\right]-[-\sin x]=0-(-1)\Rightarrow \left[\sin x\right]-[-\sin x]=1$