Trigonometric functions have got large powers!

Geometry Level 5

Define Fn(x)=k=1n(sin2kx+cos2kx)F_n(x) = \prod_{k=1}^n (\sin^{2^k} x+\cos^{2^k} x)

If F2015(π6)=a2b11c2b1\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+ca+b+c.

Clarification

  • The power of aa in numerator is 2b12^{b-1} whereas the power of cc in denominator is 2b12^b-1

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

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