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UPSC NDA 2 2012 Mathematics Paper
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© examsnet.com
Question : 38
Total: 120
If
s
i
n
A
=
2
√
5
and
cos
B
=
1
√
10
where
A
and
B
are acute angles, then what is
A
+
B
equal to?
135
∘
90
∘
75
∘
60
∘
Validate
Solution:
s
i
n
A
=
2
√
5
∴
cos
A
=
√
1
−
s
i
n
2
A
=
√
1
−
4
5
=
1
√
5
cos
B
=
1
√
10
∴
s
i
n
B
=
√
1
−
cos
2
B
=
3
√
10
s
i
n
(
A
+
B
)
=
s
i
n
A
×
cos
B
+
cos
A
×
s
i
n
B
=
2
√
5
×
1
√
10
+
1
√
5
×
3
√
10
=
2
5
√
2
+
3
5
√
2
=
5
5
√
2
=
1
√
2
s
i
n
(
A
+
B
)
=
s
i
n
π
4
A
+
B
=
45
∘
or
135
∘
.
© examsnet.com
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