# Is There Any Inverse Trigonometric Identity?

Geometry Level 4

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

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

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