If \( f(x)=\left\{\begin{array}{ll}m x+1, & x \leq \frac{\pi}{2} \\ \sin x+n, & x\frac{\pi}{2}\e...
If \( f(x)=\left\{\begin{array}{ll}m x+1, & x \leq \frac{\pi}{2} \\ \sin x+n, & x\frac{\pi}{2}\end{array}\right. \) is continuous at \( x=\frac{\pi}{2} \), then
(A) \( m=1, n=0 \)
(B) \( m=\frac{n \pi}{2}+1 \)
(C) \( n=m \frac{\pi}{2} \)
(D) \( m=n=\frac{\pi}{2} \)
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