I'm Nina. I have a really tough homework that counts as a test and I couldn't do it. It's really urgent. Help please!
Let $\alpha \in \Bbb{R}^+$. Let $F$ be the function defined in $\Bbb{R}$ by $F(x) = \frac{1}{\cosh\alpha - \cos x}.$ What is the decomposition into simple elements of the fraction? $ -\frac{2X}{X^2 - (e^{\alpha}+ e^{-\alpha} )X+1} $
Give an other expression for $\displaystyle -\frac{e^{\alpha}}{e^{ix} - e^{\alpha}}$.
And for $\displaystyle -\frac{e^{\alpha}}{e^{ix} - e^{-\alpha}}$.
And big thanks.