Is There Any Inverse Trigonometric Identity?

Geometry Level 4

f(x)=(arcsin(x))3+(arccos(x))3\large \displaystyle f(x) = (\arcsin(x))^3 + (\arccos(x))^3

If the sum of the maximum and minimum values of the function f ⁣:RR f \colon \mathbb R \to \mathbb R can be expressed as aπbc\displaystyle \dfrac{a { \pi}^{b}}{c}, where a,ba,b and cc are positive integers with a,ca,c coprime, find a+b+ca+b+c.

Belated Happy Pi Day!
Based on a 12 Standard Math problem

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