# Denominators are cubed

Geometry Level 3

Given that $$\dfrac{\sin^4 x}{2}+\dfrac{\cos^4 x}{3}=\dfrac{1}{5}$$ and $$\dfrac{\sin^8x}{8}+\dfrac{\cos^8x}{27}$$ which can be expressed as $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

×