# Expo-Trig equation

Geometry Level 3

$\large 81^{\sin^2{x}} + 81^{\cos^2{x}} = 30$

If $$A$$ and $$B$$ are the two values of $$x \in \left[0, \frac{\pi}{2}\right]$$ such that the equation above is fulfilled, find the value of $$\dfrac{\pi}{A+B}$$.

×