What is the proof for this formula: $$ \cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2 = 1, $$ where $\alpha$, $\beta$ and $\gamma$ are the angles between a vector and the base of a right-handed orthonormal base in Euclidean space? I can't seem to find a solid proof.
2026-04-28 11:15:55.1777374955
Proof for $\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2 = 1$ in Euclidean space
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Hint: Use the inner/dot product interpretation of these angles. Then the statement becomes immediate.