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

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Consider the two curves \( c_{1}: y=1+\cos x \) and
\( \mathrm{P} \)
\( c_{2}: y=1+\cos (x-\alpha) \) for \( \alpha \in\left(0, \frac{\pi}{2}\right) \), where
W
\( x \in[0, \pi] \). Also the area of the figure bounded by the curve \( c_{1}, c_{2} \) and \( x=0 \) is same as that of the figure bounded by \( c_{2}, y=1 \) and \( x=\pi \).

The value of \( \alpha \) is
(1) \( \frac{\pi}{4} \)
(2) \( \frac{\pi}{3} \)
(3) \( \frac{\pi}{6} \)
(4) \( \frac{\pi}{8} \)
.


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