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JEE Main Math Class 11 Sequences and Series Part 1 Questions
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© examsnet.com
Question : 9
Total: 100
The sum of all values of
θ
∈
(
0
,
π
2
)
satisfying
sin
2
2
θ
+
cos
4
2
θ
=
3
4
is:
[Jan. 10, 2019 (I)]
π
5
π
4
π
2
3
π
8
Validate
Solution:
sin
2
2
θ
+
cos
4
2
θ
=
3
4
⇒
1
−
cos
2
2
θ
+
cos
4
2
θ
=
3
4
⇒
cos
2
2
θ
(
1
−
cos
2
2
θ
)
=
1
4
. . . (i)
∵
G.M.
≤
A.M.
∴
(
cos
2
2
θ
)
(
1
−
cos
2
2
θ
)
≤
(
cos
2
2
θ
+
(
1
−
cos
2
2
θ
2
)
2
=
1
4
. . . (ii)
So, from equation (i) and (ii), we get.
G.M.
=
A.M.
It is possible only if
cos
2
2
θ
=
1
−
cos
2
2
θ
⇒
cos
2
2
θ
=
1
2
⇒
cos
2
θ
=
±
1
√
2
⇒
θ
=
π
8
,
3
π
8
∴
Sum
=
π
8
+
3
π
8
=
π
2
© examsnet.com
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