Question:medium

If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \( \cos\alpha + \cos^2\beta = \)

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For a cube, you can memorize these standard angles: - Angle between two body diagonals: \( \cos^{-1}(1/3) \). - Angle between a body diagonal and a face diagonal: \( \cos^{-1}(\sqrt{2/3}) \). - Angle between a body diagonal and an edge: \( \cos^{-1}(1/\sqrt{3}) \).

Updated On: Mar 30, 2026

\( \frac{5}{9} \)
\( \frac{2}{9} \)
1
\( \frac{2}{3} \)

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The Correct Option is C

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