jee-main 2023 Q66

jee-main · India · session2_10apr_shift2 Trigonometric equations in context
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 $\beta = \sum _ { x \in S } \tan ^ { 2 } \frac { x } { 3 }$, then $\frac { 1 } { 6 } ( \beta - 14 ) ^ { 2 }$ is equal to
(1) 16
(2) 8
(3) 64
(4) 32
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 $\beta = \sum _ { x \in S } \tan ^ { 2 } \frac { x } { 3 }$, then $\frac { 1 } { 6 } ( \beta - 14 ) ^ { 2 }$ is equal to\\
(1) 16\\
(2) 8\\
(3) 64\\
(4) 32