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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 2
Total: 120
If
tan
−
1
(
2
)
,
tan
−
1
(
3
)
are two angles of a triangle, then what is the third angle?
3π/4
π/4
π/3
π/6
Validate
Solution:
Given:
tan
−
1
(
2
)
,
tan
−
1
(
3
)
are two angles of a triangle
Let, C be the third angles of a triangle.
As we know, sum of angle in triangle is equal to 180°
So,
tan
−
1
(
2
)
+
tan
−
1
(
3
)
+
C
=
π
tan
−
1
2
+
3
1
−
(
2
)
(
3
)
+
C
=
π
=
tan
−
1
5
−
5
+
C
=
π
⇒
tan
−
1
(
−
1
)
+
C
=
π
⇒
3
π
∕
4
+
C
=
π
⇒
C
=
π
−
3
π
∕
4
=
π
∕
4
Hence, option ( 2 ) is correct.
© examsnet.com
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