Oh k !

Calculus Level 3

\[ \large \frac{\displaystyle \int_0^{\pi/2} (\cos x)^{\sqrt{2} + 1} dx}{\displaystyle \int_0^{\pi/2} (\cos x)^{ \sqrt{2} - 1} dx}= k - \sqrt{k}\]

Find \(k\).

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