Trigonometry! #31

Geometry Level 4

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

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

This problem is part of the set Trigonometry.

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