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Question
Mathematics
The number of solutions of the equation cos (x+(π/3)) cos ((π/3)-x)=(1/4) cos 2 2 x, x ∈[-3 π, 3 π] is :
Q. The number of solutions of the equation
cos
(
x
+
3
π
)
cos
(
3
π
−
x
)
=
4
1
cos
2
2
x
,
x
∈
[
−
3
π
,
3
π
]
is :
1039
166
JEE Main
JEE Main 2022
Trigonometric Functions
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A
8
0%
B
5
25%
C
6
25%
D
7
50%
Solution:
cos
(
3
π
+
x
)
cos
(
3
π
−
x
)
=
4
1
cos
2
2
x
x
∈
[
−
3
π
,
3
π
]
4
(
cos
2
(
3
π
)
−
sin
2
x
)
=
cos
2
2
x
4
(
4
1
−
sin
2
x
)
=
cos
2
2
x
1
−
4
sin
2
x
=
cos
2
2
x
1
−
2
(
1
−
cos
2
x
)
=
cos
2
2
x
let
cos
2
x
=
t
−
1
+
2
cos
2
x
=
cos
2
2
x
t
2
−
2
t
+
1
=
0
(
t
−
1
)
2
=
0
t
=
1
cos
2
x
=
1
2
x
=
2
nπ
x
=
nπ
n
=
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3