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JEE Advanced Model Paper 2 with solutions for online practice
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© examsnet.com
Question : 40
Total: 54
f(x) =
c
o
s
2
x
+
c
o
s
2
(
π
3
+
x
)
- cosx cos
(
π
3
+
x
)
is
an odd function
an even function
a periodic function
f(0) = f(1)
Validate
Solution:
f(x) =
1
2
[
(
1
+
c
o
s
2
x
)
+
(
1
+
x
o
s
(
2
π
3
+
2
x
)
−
{
c
o
s
(
π
3
+
2
x
)
+
c
o
s
π
3
}
)
]
=
1
2
[
3
2
+
c
o
s
2
x
+
c
o
s
(
2
π
3
+
2
x
)
−
x
o
s
(
π
3
+
2
x
)
]
=
1
2
[
3
2
+
2
x
o
s
(
2
x
+
π
3
)
c
o
s
π
3
−
c
o
s
(
π
3
+
2
x
)
]
f(x) =
3
4
∴ f(x) is an even function, a periodic function and f(0) = f(1) =
3
4
© examsnet.com
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