\[f(x)=e^{\sin(x)}\cos(x)\]
###### This is part of the set Trevor's Ten

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

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

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