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UPSC NDA II 2011 Mathematics Paper
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© examsnet.com
Question : 34
Total: 120
In a triangle
ABC
, if
A
=
tan
−
1
2
and
B
=
tan
−
1
3
, then
C
is equal to
π
3
π
4
π
6
π
2
Validate
Solution:
tan
A
=
2
and
tan
B
=
3
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
−
tan
A
⋅
tan
B
=
2
+
3
1
−
6
=
5
−
5
=
−
1
∵
A
+
B
+
C
=
π
A
+
B
=
π
−
C
tan
(
A
+
B
)
=
tan
(
π
−
C
)
=
−
tan
C
∴
−
tan
C
=
−
1
⇒
tan
C
=
tan
π
4
∴
C
=
π
4
.
© examsnet.com
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