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Mathematics
Mathematics
Problem
If
sin
α
+
sin
β
=
a
\sin \alpha + \sin \beta = a
sin
α
+
sin
β
=
a
and
cos
α
+
cos
β
=
b
\cos \alpha + \cos \beta = b
cos
α
+
cos
β
=
b
, then show that
tan
(
α
−
β
2
)
=
±
4
−
a
2
−
b
2
a
2
+
b
2
\tan\left(\frac{\alpha - \beta}{2}\right) = \pm \sqrt{\frac{4 - a^2 - b^2}{a^2 + b^2}}
tan
(
2
α
−
β
)
=
±
a
2
+
b
2
4
−
a
2
−
b
2
.
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