If $\alpha$ and $\beta$ are real numbers such that $\sec ^2\left(\tan ^{-1}(\alpha)\right)+\operatorname{cosec}^2\left(\cot ^{-1}(\beta)\right)=36$ and $\alpha+\beta=8$, then $\left(\alpha^2+\beta\right)$ is $(\alpha\beta)$ (24 Jan, Shift I, Memory Based)

Question

If $\alpha$ and $\beta$ are real numbers such that $\sec ^2\left(\tan ^{-1}(\alpha)\right)+\operatorname{cosec}^2\left(\cot ^{-1}(\beta)\right)=36$ and $\alpha+\beta=8$, then $\left(\alpha^2+\beta\right)$ is $(\alpha>\beta)$ (24 Jan, Shift I, Memory Based)

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If \(\alpha\) and \(\beta\) are real numbers such that \(\sec ^2\left(\tan ^{-1}(\alpha)\right)+\operatorname{cosec}^2\l…

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