Sabendo que $2\mathrm{sen}(\alpha +\beta )=\mathrm{sen}(\alpha )+\mathrm{sen}(\beta )$, com $\alpha +\beta \ne \pi k,k\in \mathbb{Z}$, assinale a opção que apresenta o valor de $\mathrm{tg}\left(\frac{\alpha }{2}\right)\cdot \mathrm{tg}\left(\frac{\beta }{2}\right)$