If a \( \sin x+b \cos (c+x)+b \cos (c-x)=\alpha, a\alpha \), then t...

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If a \( \sin x+b \cos (c+x)+b \cos (c-x)=\alpha, a\alpha \), then the minimum value of \( |\cos c| \) is:
\( \mathrm{P} \)
(a) \( \sqrt{\frac{\alpha^{2}-a^{2}}{b^{2}}} \)
(b) \( \sqrt{\frac{\alpha^{2}-a^{2}}{2 b^{2}}} \)
(c) \( \sqrt{\frac{\alpha^{2}-a^{2}}{3 b^{2}}} \)
(d) \( \sqrt{\frac{\alpha^{2}-a^{2}}{4 b^{2}}} \)
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