Maximizing and minimizing inverse trigo functions
Geometry
Level
5
\[\large f(x) = {\left(\sin^{-1}x\right)}^3 + {\left(\cos^{-1}x\right)}^3\]
For real \(x\), if the sum of the minimum and maximum values of the function above can be represented as \(\dfrac{a}{b} \pi^3\), where \(a\) and \(b\) are coprime positive integers, then what is the value of \(a+b\)?
by
Tapas Mazumdar