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As shown in the figure, \( A D \) is the altitude on \( B C \) and \( A D \) produced meets the circumcircle of \( \triangle A B C \) at \( P \) where \( D P=x \). Similarly, \( E Q=y \) and \( F R=z \). If \( a, b, c \) respectively denotes the sides \( B C, C A \) and \( A B \), then \( \frac{a}{2 x}+\frac{b}{2 y}+\frac{c}{2 z} \) has the value equal to
(a) \( \tan A+\tan B+\tan C \)
(b) \( \cot A+\cos B+\cot C \)
(c) \( \cos A+\cos B+\cos C \)
(d) \( \operatorname{cosec} A+\operatorname{cosec} B+\operatorname{cosec} C \)
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