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If $f(z)= u - iv$ is an analytic function of $z = x + iy$ and $u-v=\Large\frac{e^y-\cos x+\sin x}{\cosh y - \cos y}$, find $f(z)$ subject to condition, $f\left(\frac{\pi}2\right)=\large \frac{3 - i}2$.

I haven't solved such problems before, I tried to use $\cosh y = \frac{e^y + e^{-y}}2$ but it didn't help.

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