The Greatest Sin

Calculus Level 4

f(x)=esin(x)cos(x)f(x)=e^{\sin(x)}\cos(x)

Let f(x)f(x) denote the function of the expression above. If the greatest possible value of f(x)f(x) can be represented by the form (cba)1aecba\left(\dfrac{\sqrt{c}-b}{a}\right)^{\large\frac{1}{a}} \cdot e^{\stackrel{\large\frac{\sqrt{c}-b}{a}}{}}

Where a,b,ca,b,c are constants and e2.7183...e\approx 2.7183... (Euler's constant) and a,b,ca,b,c are integers. Find a+b+ca+b+c.

This is part of the set Trevor's Ten
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