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UPSC 2016 CDS II Math Paper
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© examsnet.com
Question : 83
Total: 100
Consider the following :
1.
c
o
s
75
°
s
i
n
15
°
+
s
i
n
12
°
c
o
s
78
°
−
c
o
s
18
°
s
i
n
72
°
=
1
2.
c
o
s
35
°
s
i
n
55
°
−
s
i
n
11
°
c
o
s
79
°
+
c
o
s
28
°
c
o
s
e
c
62
°
=
1
3.
s
i
n
18
°
c
o
s
18
°
−
s
i
n
59
°
s
e
c
31
°
=
0
Which of the above are correct ?
[2016 CDS-II]
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Validate
Solution:
cos
75
∘
sin
15
∘
+
sin
12
∘
cos
78
∘
−
cos
18
∘
sin
72
∘
=
sin
15
∘
sin
15
∘
+
cos
78
∘
cos
78
∘
−
sin
72
∘
sin
72
∘
=
1
+
1
−
1
=
1
Hence 1 is correct
cos
35
∘
sin
55
∘
−
sin
11
∘
cos
79
∘
+
cos
28
∘
cosec
62
∘
=
cos
(
90
∘
−
55
∘
)
sin
55
∘
−
sin
(
90
∘
−
79
∘
)
cos
79
∘
+
cos
(
90
∘
−
62
∘
)
sin
62
∘
=
sin
55
∘
sin
55
∘
−
cos
79
∘
cos
79
∘
+
sin
62
∘
sin
62
∘
=
1
−
1
+
1
=
1
Hence, 2 is correct
sin
80
∘
cos
10
∘
−
sin
59
∘
sec
31
∘
=
sin
(
90
∘
−
10
∘
)
cos
10
∘
−
sin
(
90
∘
−
31
∘
)
cos
31
∘
=
cos
10
∘
cos
10
∘
−
cos
31
∘
cos
31
∘
=
1
−
1
=
0
Hence, 3 is correct.
© examsnet.com
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