# More trigonometry I guess?

Geometry Level 4

$\large \dfrac1{\cos \alpha} + \dfrac1{\cos\beta} + \dfrac1{\cos \gamma} \geq \dfrac{M \cdot R}{R+r}$

Let $$r$$ and $$R$$ denote the incircle and circumcircle, respectively, of an acute-angle triangle with interior angles $$\alpha, \beta$$ and $$\gamma$$.

Find the maximum value of $$M$$ satisfying the inequality above.

×