Let X be a r.v. with density $\displaystyle f(x)=(1-|x|)1_{(-1,1)}(x)$. How do I show that $\displaystyle \varphi(u)=\frac{2(1-cosu)}{u^2}$.

Am i on the right track to relate it with $\displaystyle cosx=\frac{1}{2}(e^{ix}+e^{-ix})$ and $\displaystyle sinx=\frac{1}{2i}(e^{ix}-e^{-ix})$