Nếu \(\tan \frac{\beta }{2} = 4\tan \frac{\alpha }{2}\) thì \(\tan \frac{{\beta  - \alpha }}{2}\) bằng :

* Hướng dẫn giải

Ta có \(\tan \frac{{\beta  - \alpha }}{2} = \frac{{\tan \frac{\beta }{2} - \tan \frac{\alpha }{2}}}{{1 + \tan \frac{\beta }{2}.\tan \frac{\alpha }{2}}} = \frac{{3\tan \frac{\alpha }{2}}}{{1 + 4{{\tan }^2}\frac{\alpha }{2}}} = \frac{{3\sin \frac{\alpha }{2}.\cos \frac{\alpha }{2}}}{{1 + 3{{\sin }^2}\frac{\alpha }{2}}} = \frac{{3\sin \alpha }}{{5 - 3\cos \alpha }}.\)