If [ $\cdot]$ denotes greatest integer function, then $\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{[\sin x]-[\cos x]+1}{2}=$

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Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow \frac{\pi^{+}}{2}} \frac{[\sin x]-[\cos x]+1}{2} \ & =\frac{0-(-1)+1}{2} \quad\left[\begin{array}{l}	ext { For } x>\frac{\pi}{2}, 0 \leq \sin x < 1 \ 	ext { and }-1 \leq \cos x < 0\end{array}ight] \ & =\frac{2}{2}=1\end{aligned}$

If [ $\cdot]$ denotes greatest integer function, then $\lim _{x \rightarrow \frac{\pi^{+}}{2}} \frac{[\sin…

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