JEE Main 2022Inverse Trigonometric FunctionsInverse Trigonometric FunctionsEasyQuestionIf for some α,β;α≤β,α+β=8\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8α,β;α≤β,α+β=8 and sec2(tan−1α)+cosec2(cot−1β)=36\sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)=36sec2(tan−1α)+cosec2(cot−1β)=36, then α2+β\alpha^2+\betaα2+β is __________Answer: 1Hide SolutionSolutionIf(tan(tan−1(α))+1(cot(cot−1β))2=36α2+β2=34αβ=15α=3,β=5∴α2+β=9+5=14\begin{aligned} & \operatorname{If}\left(\tan \left(\tan ^{-1}(\alpha)\right)+1\left(\cot \left(\cot ^{-1} \beta\right)\right)^2=36\right. \\ & \alpha^2+\beta^2=34 \\ & \alpha \beta=15 \\ & \alpha=3, \beta=5 \\ & \therefore \alpha^2+\beta=9+5=14 \end{aligned}If(tan(tan−1(α))+1(cot(cot−1β))2=36α2+β2=34αβ=15α=3,β=5∴α2+β=9+5=14