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Mathematics
Mathematics
Problem
If
α
+
β
+
γ
=
π
\alpha + \beta + \gamma = \pi
α
+
β
+
γ
=
π
and
tan
1
4
(
β
+
γ
−
α
)
tan
1
4
(
γ
+
α
−
β
)
tan
1
4
(
α
+
β
−
γ
)
=
1
,
\tan \frac{1}{4}(\beta + \gamma - \alpha) \tan \frac{1}{4}(\gamma + \alpha - \beta) \tan \frac{1}{4}(\alpha + \beta - \gamma) = 1,
tan
4
1
(
β
+
γ
−
α
)
tan
4
1
(
γ
+
α
−
β
)
tan
4
1
(
α
+
β
−
γ
)
=
1
,
then prove that
1
+
cos
α
+
cos
β
+
cos
γ
=
0
1 + \cos \alpha + \cos \beta + \cos \gamma = 0
1
+
cos
α
+
cos
β
+
cos
γ
=
0
.
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