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Problem
Problem
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive, show that
tan
−
1
a
(
a
+
b
+
c
)
b
c
+
tan
−
1
b
(
a
+
b
+
c
)
a
c
+
tan
−
1
c
(
a
+
b
+
c
)
a
b
=
π
\tan^{-1} \sqrt{\frac{a(a+b+c)}{bc}} + \tan^{-1} \sqrt{\frac{b(a+b+c)}{ac}} + \tan^{-1} \sqrt{\frac{c(a+b+c)}{ab}} = \pi
tan
−
1
b
c
a
(
a
+
b
+
c
)
+
tan
−
1
a
c
b
(
a
+
b
+
c
)
+
tan
−
1
ab
c
(
a
+
b
+
c
)
=
π
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