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Gaokao Math Practice Question

直三棱柱 $A B C-A_{1} B_{1} C_{1}$ 中, $\angle B C A=90^{\circ}, M, N$ 分别是 $A_{1} B_{1}, A_{1} C_{1}$ 的 中点, $B C=C A=C C_{1}$, 则 $B M$ 与 $A N$ 所成角的余弦值为 ($\qquad$)

  1. A.$\frac{1}{10}$
  2. B.$\frac{2}{5}$
  3. C.$\frac{\sqrt{30}}{10}$
  4. D.$\frac{\sqrt{2}}{2}$

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