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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 50
Total: 100
If
A
=
s
i
n
45
°
−
s
i
n
30
°
c
o
s
45
°
+
c
o
s
60
°
and
B
=
s
e
c
45
°
−
t
a
n
45
°
c
o
s
e
c
45
°
+
c
o
t
45
°
,
then which one of the following is correct ?
[2017 CDS-II]
A = B
A > B > 0
A < B
B < A < 0
Validate
Solution:
A
=
sin
45
°
−
sin
30
°
cos
45
°
+
cos
60
°
=
(
1
√
2
−
1
2
)
(
1
√
2
+
1
2
)
=
(
√
2
−
1
2
)
(
√
2
+
1
2
)
=
√
2
−
1
√
2
+
1
B
=
sec
45
°
−
tan
45
°
cosec
45
°
+
cot
45
°
=
√
2
−
1
√
2
+
1
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