Let S = {x ∈(-π/2, π/2) : 9^(1-tan^2x) + 9^(tan^2x) = 10}

Question

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

(1) 32 

(2) 8 

(3) 64 

(4) 16

Answer 1

Correct option is (1) 32