If $f(x)=\left \{\begin{array}{1 1}mx+1, & if\;x\leq\large\frac{\pi}{2}\\\sin x+n, & if\;x>\large\frac{\pi}{2}\end{array}\right.$,is continuous at $x=\large\frac{\pi}{2}$,then

Question

$$\begin{array}{1 1}(A)\;m=1,n=0 & (B)\;m=\large\frac{n\pi}{2}+1\\(C)\;n=\large\frac{m\pi}{2} & (D)\;m=n=\large\frac{\pi}{2}\end{array}$$