Comprehension \( \alpha \) is a root of the equation \( 2 \sin x \) \( +\sin 2 x=1+\cos x, \beta...

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Comprehension
\( \alpha \) is a root of the equation \( 2 \sin x \)
\( +\sin 2 x=1+\cos x, \beta \) is a root of the equation \( 3 \cos ^{2} x-10 \cos x+ \)
\( 3=0 \) and \( \gamma \) is a root of the equation \( 1+\sin x=\cos x(1+2 \sin x) \),
\( 0 \leq \alpha, \beta, \gamma \leq \pi / 2 \), then on the basis of above information answer the following questions
\( \cos \alpha \times \cos \beta \times \cos \gamma \) is equal to
(a) \( \frac{1}{2 \sqrt{3}} \)
(b) \( \frac{1}{\sqrt{3}} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{\sqrt{2}} \)
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