Tính (sin alpha + sin betac.cos(alpha + beta))/((cos alpha - sin beta.sin(alpha + beta

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} \frac{\sin \alpha +\sin \beta \cos \left(\alpha +\beta \right)}{\cos \alpha -\sin \beta \sin \left(\alpha +\beta \right)} \\ =\frac{\sin \alpha +\frac{1}{2}\left[\sin \left(\alpha +2\beta \right)+\sin (-\alpha )\right]}{\cos \alpha +\frac{1}{2}\left[\cos \left(\alpha +2\beta \right)-\cos (-\alpha )\right]} \\ =\frac{\sin \alpha +\frac{1}{2}\left[\sin \left(\alpha +2\beta \right)-\sin \left(\alpha \right)\right]}{\cos \alpha +\frac{1}{2}\left[\cos \left(\alpha +2\beta \right)-\cos \left(\alpha \right)\right]} \\ =\frac{\sin \left(\alpha +2\beta \right)+\sin \left(\alpha \right)}{\cos \left(\alpha +2\beta \right)+\cos \left(\alpha \right)} \\ =\frac{2\sin \left(\alpha +\beta \right)\cos \beta }{2\cos \left(\alpha +\beta \right)\cos \beta }=\tan \left(\alpha +\beta \right) \end{gathered}$$