Let S = { x ∈ ( -π/2, π/2): 9^(1 - tan² x) + 9^(tan² x) = 10 } an… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 10 April, Shift 2Trigonometric Equations

Let $S = \left\{ x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) : 9^{1 - \tan^2 x} + 9^{\tan^2 x} = 10 \right\}$ and $\beta = \sum_{x \in S} \tan^2 \left( \frac{x}{3} \right)$ , then $\frac{1}{6}\left( \beta - 14 \right)^2$ is equal to:

A
$16$
B
$32$
C
$8$
D
$64$

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