Consider the two curves \( C_{1}: y=1+\cos x \) and \( C_{2}: y=1 \) \( +\cos (x-\alpha) \) for ...

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Consider the two curves \( C_{1}: y=1+\cos x \) and \( C_{2}: y=1 \) \( +\cos (x-\alpha) \) for \( \alpha \in\left(0, \frac{\pi}{2}\right) ; x \in[0, \pi] \). the value of \( \alpha \), for which the area of the figure bounded by the curves \( C_{1}, C_{2} \) and \( x=0 \) is same as that of the figure bounded by \( C_{2}, y=1 \) and \( x=\pi \).
(a) \( \pi / 3 \)
(b) \( \pi / 6 \)
(c) \( \pi / 4 \)
(d) \( \pi / 12 \)
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