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Tardigrade
Question
Mathematics
Let S = θ ∈[0,2 π]: 82 sin 2 θ+82 cos 2 θ=16 . Then n ( S )+ displaystyle∑θ ∈ S ( sec ((π/4)+2 θ) operatornamecosec((π/4)+2 θ)) is equal to:
Q. Let
S
=
{
θ
∈
[
0
,
2
π
]
:
8
2
s
i
n
2
θ
+
8
2
c
o
s
2
θ
=
16
}
.
Then
n
(
S
)
+
θ
∈
S
∑
(
sec
(
4
π
+
2
θ
)
cosec
(
4
π
+
2
θ
)
)
is equal to:
440
131
JEE Main
JEE Main 2022
Sets
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A
0
31%
B
−
2
33%
C
−
4
19%
D
12
17%
Solution:
8
2
s
i
n
2
θ
+
8
2
−
2
s
i
n
2
θ
=
16
y
+
y
64
=
16
⇒
y
=
8
⇒
sin
2
θ
=
1/2
n
(
S
)
+
θ
∈
S
∑
cos
(
π
/4
+
2
θ
)
sin
(
π
/4
+
2
θ
)
1
=
4
+
(
−
2
)
×
4
=
−
4