The equation \( (\cos p-1) x^{2}+\cos p x+\sin p=0 \), in variable \( x \), has real roots. Then...

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The equation \( (\cos p-1) x^{2}+\cos p x+\sin p=0 \), in variable \( x \), has real roots. Then, \( p \) belongs to the interval
(A) \( (0,2 \pi) \)
(B) \( (-8,0) \)
(C) \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
(D) \( (0, \pi) \)
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