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UPSC NDA I 2014 Mathematics Paper
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© examsnet.com
Question : 41
Total: 120
What is the value of cos 36°?
[NDA I 2014]
√
5
−
1
4
√
5
+
1
4
√
10
+
2
√
5
4
√
10
−
2
√
5
4
Validate
Solution:
Let
x
=
36
°
⇒
5
x
=
180
°
⇒
3
x
=
180
°
−
2
x
⇒
s
i
n
3
x
=
s
i
n
2
x
⇒
3
s
i
n
x
−
4
s
i
n
3
x
=
2
s
i
n
x
c
o
s
x
⇒
3
−
4
s
i
n
2
x
=
2
c
o
s
x
⇒
3
−
4
+
4
c
o
s
2
x
=
2
c
o
s
x
⇒
4
c
o
s
2
x
−
2
c
o
s
−
1
=
0
⇒
c
o
s
x
=
1
+
√
5
4
⇒
c
o
s
36
°
=
1
+
√
5
4
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