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Problems
Let
S
=
{
x
∈
(
−
π
2
,
π
2
)
:
9
1
−
tan
2
x
+
9
tan
2
x
=
10
}
S = \left\{ x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10 \right\}
S
=
{
x
∈
(
−
2
π
,
2
π
)
:
9
1
−
t
a
n
2
x
+
9
t
a
n
2
x
=
10
}
…
Mathematics
Problem
Let
S
=
{
x
∈
(
−
π
2
,
π
2
)
:
9
1
−
tan
2
x
+
9
tan
2
x
=
10
}
S = \left\{ x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10 \right\}
S
=
{
x
∈
(
−
2
π
,
2
π
)
:
9
1
−
t
a
n
2
x
+
9
t
a
n
2
x
=
10
}
and
β
=
∑
x
∈
S
tan
2
(
x
3
)
\beta = \sum_{x \in S} \tan^2 \left( \frac{x}{3} \right)
β
=
∑
x
∈
S
tan
2
(
3
x
)
, then
1
6
(
β
−
14
)
2
\frac{1}{6}(\beta - 14)^2
6
1
(
β
−
14
)
2
is equal to (a) 32 (b) 8 (c) 64 (d) 16
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