# Trigonometric functions have got large powers!

Geometry Level 5

Define $F_n(x) = \prod_{k=1}^n (\sin^{2^k} x+\cos^{2^k} x)$

$\text{If}\ F_{2015}\left(\frac{\pi}{6}\right) = \frac{a^{2^{b-1}}-1}{c^{2^b-1}}$

Then find the value of $$a+b+c$$.

Clarification

• The power of $$a$$ in numerator is $$2^{b-1}$$ whereas the power of $$c$$ in denominator is $$2^b-1$$

• $$a,\ b,\ c$$ are positive integers.

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