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JEE Main Math Class 11 Trigonometric Functions Questions
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© examsnet.com
Question : 6
Total: 115
Let
|
cos
θ
cos
(
60
−
θ
)
cos
(
60
−
θ
)
|
≤
1
8
,
θ
∈
[
0
,
2
π
]
Then, the sum of all
θ
∈
[
0
,
2
π
]
, where
cos
3
θ
attains its maximum value, is :
[9 Apr 2024 Shift 1]
9
π
18
π
6
π
15
π
Validate
Solution:
👈: Video Solution
We know that
(
cos
θ
)
(
c
o
s
(
6
0
∘
−
θ
)
(
cos
(
60
∘
+
θ
)
=
1
4
cos
3
θ
.
.
So equation reduces to
|
1
4
cos
3
θ
|
≤
1
8
⇒
|
cos
3
θ
|
≤
1
2
⇒
−
1
2
≤
cos
3
θ
≤
1
2
⇒
maximum value of
cos
3
θ
=
1
2
, here
⇒
3
θ
=
2
n
π
±
π
3
θ
=
2
n
π
3
±
π
9
As
θ
∈
[
0
,
2
π
]
possible values are
θ
=
{
π
9
,
5
π
9
,
7
π
9
,
11
π
9
,
13
π
9
,
17
π
9
}
Whose sum is
π
9
+
5
π
9
+
7
π
9
+
11
π
9
+
13
π
9
+
17
π
9
=
54
π
9
=
6
π
© examsnet.com
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