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UPSC NDA Math Model Paper 5
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© examsnet.com
Question : 117
Total: 120
Find the value of
cos
2
x
+
cos
2
(
x
+
π
6
)
+
cos
2
(
x
−
π
6
)
.
3
−
2
cos
2
x
2
3
+
2
sin
2
x
2
3
+
2
cos
2
x
2
None of the above
Validate
Solution:
We have to find the value of
cos
2
x
+
cos
2
(
x
+
π
6
)
+
cos
2
(
x
−
π
6
)
Rewrite the given expression by using double angle formula as follows:
cos
2
x
+
cos
2
(
x
+
π
6
)
+
cos
2
(
x
−
π
6
)
=
1
+
cos
2
x
2
+
1
+
cos
(
2
x
+
π
3
)
2
+
1
+
cos
(
2
x
−
π
3
)
2
=
1
2
+
1
2
+
1
2
+
1
2
[
cos
2
x
+
cos
(
2
x
+
π
3
)
+
cos
(
2
x
−
π
3
)
]
=
1
2
[
3
+
cos
2
x
+
2
cos
2
x
cos
(
π
3
)
]
[
∵
cos
x
+
cos
y
=
2
cos
(
x
+
y
2
)
cos
(
x
−
y
2
)
]
=
3
+
2
cos
2
x
2
© examsnet.com
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