Trigonometry! #31

Geometry Level 4

Find the value of cos(2cos1x+sin1x)\cos(2\cos^{-1}x + \sin^{-1}x) at x=15x=\frac {1}{5}, where 0cos1xπ0≤\cos^{-1}x≤\pi and π2sin1xπ2\frac {-\pi}{2} ≤ \sin^{-1}x ≤ \frac {\pi}{2}.

If your answer is in the form of abc-\frac {a\sqrt{b}}{c}, where bb is a square free integer, enter the value of a+b+ca+b+c.

This problem is part of the set Trigonometry.

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