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Mathematics
Mathematics
Problem
If
sin
α
sin
β
=
cos
γ
cos
δ
\frac{\sin \alpha}{\sin \beta} = \frac{\cos \gamma}{\cos \delta}
s
i
n
β
s
i
n
α
=
c
o
s
δ
c
o
s
γ
, then
sin
(
α
−
β
2
)
⋅
cos
(
α
+
β
2
)
⋅
cos
δ
sin
(
δ
−
γ
2
)
⋅
sin
(
δ
+
γ
2
)
⋅
sin
β
\frac{\sin \left( \frac{\alpha - \beta}{2} \right) \cdot \cos \left( \frac{\alpha + \beta}{2} \right) \cdot \cos \delta}{\sin \left( \frac{\delta - \gamma}{2} \right) \cdot \sin \left( \frac{\delta + \gamma}{2} \right) \cdot \sin \beta}
s
i
n
(
2
δ
−
γ
)
⋅
s
i
n
(
2
δ
+
γ
)
⋅
s
i
n
β
s
i
n
(
2
α
−
β
)
⋅
c
o
s
(
2
α
+
β
)
⋅
c
o
s
δ
is equal to
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