A line makes angles ,

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A line makes angles α\alpha, β\beta, γ\gamma and δ\delta with the four diagonals of a cube; prove that cos⁡2α+cos⁡2β+cos⁡2γ+cos⁡2δ=43\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma + \cos^2 \delta = \frac{4}{3}

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