# The Greatest Sin

Calculus Level 4

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

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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