# Confusing sines and cosines

Level pending

The value of $\cos^{2} 55^{\circ} +\cos 55^{\circ} \cos 35^{\circ} \sin 10^{\circ} + \sin 20^{\circ} \cos^{2} 5^{\circ}$ can be expressed as a fraction $$\frac{a}{b}$$, while $$a$$ and $$b$$ are positive integers which are relatively prime. Find $$a+b$$.

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