If for some , ; , + =8 and ^2( ^-1 )+ ^2( ^-1 )=36, then ^2+ is __________ Answer: 14

Question

If for some $\alpha ,\beta ;\alpha \le \beta ,\alpha +\beta =8$ and ${\sec }^{2}({	an }^{-1}\alpha )+{\csc }^{2}({\cot }^{-1}\beta )=36$, then ${\alpha }^{2}+\beta $ is \_\_\_\_\_\_\_\_\_\_

Answer: 14

Accepted Answer

$\begin{gathered} If(	an ({	an }^{-1}(\alpha ))+1{(\cot ({\cot }^{-1}\beta ))}^{2}=36 \ {\alpha }^{2}+{\beta }^{2}=34 \ \alpha \beta =15 \ \alpha =3,\beta =5 \ 	herefore {\alpha }^{2}+\beta =9+5=14 \end{gathered}$

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