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A ladder rests against a wall making an angle \( \alpha \) with the horizontal. The foot of the ladder is pulled away from the wall through a distance \( x \) so that it slides a distance \( y \) down the wall making an angle \( \beta \) with the horizontal. The correct relation is
(A) \( y=x \tan \frac{\alpha+\beta}{2} \)
(B) \( x=y \tan (\alpha+\beta) \)
(C) \( x=y \tan \frac{\alpha+\beta}{2} \)
(D) \( y=x \tan (\alpha+\beta) \)
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