If $\mathrm{f}(x)=\left\{\begin{array}{ll}\operatorname{m} x+1, & x \leqslant \frac{\pi}{2} \\ \sin x+\mathrm{n}, & x>\frac{\pi}{2}\end{array}\right.$, is continuous at $x=\frac{\pi}{2},(\mathrm{~m}, \mathrm{n} \in \mathbb{Z})$ then
- A$\mathrm{m}=1, \mathrm{n}=0$
- B$\mathrm{m}=\frac{\mathrm{n} \pi}{2}$
- C$\mathrm{m}=\mathrm{n}=\frac{\pi}{2}$
- D$\mathrm{n}=\frac{\mathrm{m} \pi}{2}$
✓ Correct answer: D
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