\( A B \) is a vertical pole. The end \( A \) is on the level ground. \( C \) is the middle poin...

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\( A B \) is a vertical pole. The end \( A \) is on the level ground. \( C \) is the middle point of AB. P is a point on the level ground. The portion \( B C \) subtends an angle \( P \) at \( P \). If \( A P=n A B \), then \( \tan \beta= \)
(A) \( \frac{n}{2 n^{2}+1} \)
(B) \( \frac{n}{n^{2}-1} \)
(C) \( \frac{n}{n^{2}+1} \)
(D) none of these
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