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Question
Mathematics
The number of distinct solutions of the equation (5/4) cos 2 2 x+ cos 4 x+ sin 4 x+ cos 6 x+ sin 6 x=2 in the interval [0,2 π] is
Q. The number of distinct solutions of the equation
4
5
cos
2
2
x
+
cos
4
x
+
sin
4
x
+
cos
6
x
+
sin
6
x
=
2
in the interval
[
0
,
2
π
]
is
404
165
Trigonometric Functions
Report Error
A
8
B
4
C
6
D
2
Solution:
4
5
cos
2
2
x
+
cos
4
x
+
sin
4
x
+
cos
6
x
+
sin
6
x
=
2
⇒
4
5
cos
2
2
x
+
1
−
2
1
sin
2
2
x
+
1
−
4
3
sin
2
2
x
=
2
⇒
cos
2
2
x
=
sin
2
2
x
⇒
tan
2
2
x
=
1
Now
2
x
∈
[
0
,
4
π
]
⇒
x
=
8
π
,
8
3
π
,
8
5
π
,
8
7
π
,
8
9
π
,
8
11
π
,
8
13
π
,
8
15
π
so number of solution
=
8