In a triangle ABC, if a^2 + b^2 = 2002 B^2,then Cot A + Cot B / Cot C is ?
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a
2
+c
2
=2002b
2
By sine Rule
sinA
a
=
sinB
b
=
sinC
c
=2R
2R
a
=sinA
2R
b
=sinB
2R
c
=sinC
cotB
cotA+cotC
=
sinB
cosB
sinA
cosA
+
sinC
cosC
=
(
2R
b
)
(
2ac
a
2
+c
2
−b
2
)
(
2R
a
)
(
2bc
b
2
+c
2
−a
2
)
+
(
2R
c
)
(
2ab
a
2
+b
2
−c
2
)
=
abc
a
2
+c
2
−b
2
abc
b
2
+c
2
−a
2
+
abc
a62+b
2
−c
2
=
a
2
+c
2
−b
2
b
2
+c
2
−a
2
+a
2
+b
2
+c
2
=
2002b
2
−b
2
2b
2
=
2001b
2
2b
2
cotB
cotA+cotC
=
2001
2
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