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Mathematics
Mathematics
Problem
If
α
,
β
\alpha, \beta
α
,
β
and
γ
\gamma
γ
are real numbers, without expanding at any stage, prove that
∣
1
cos
(
β
−
α
)
cos
(
γ
−
α
)
cos
(
α
−
β
)
1
cos
(
γ
−
β
)
cos
(
α
−
γ
)
cos
(
β
−
γ
)
1
∣
=
0.
\begin{vmatrix} 1 & \cos(\beta - \alpha) & \cos(\gamma - \alpha) \\ \cos(\alpha - \beta) & 1 & \cos(\gamma - \beta) \\ \cos(\alpha - \gamma) & \cos(\beta - \gamma) & 1 \end{vmatrix} = 0.
1
cos
(
α
−
β
)
cos
(
α
−
γ
)
cos
(
β
−
α
)
1
cos
(
β
−
γ
)
cos
(
γ
−
α
)
cos
(
γ
−
β
)
1
=
0.
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