Question Number 42673 by Tawa1 last updated on 31/Aug/18
Answered by OrestesDante last updated on 15/Sep/18
$$\frac{{p}}{{q}}=\frac{{sin}\mathrm{2}\alpha+{sin}\mathrm{2}\beta}{{cos}\mathrm{2}\alpha+{cos}\mathrm{2}\beta} \\ $$$$\frac{\mathrm{2}{sin}\left(\frac{\mathrm{2}\alpha+\mathrm{2}\beta}{\mathrm{2}}\right){cos}\left(\frac{\mathrm{2}\alpha−\mathrm{2}\beta}{\mathrm{2}}\right)}{\mathrm{2}{cos}\left(\frac{\mathrm{2}\alpha+\mathrm{2}\beta}{\mathrm{2}}\right){cos}\left(\frac{\mathrm{2}\alpha−\mathrm{2}\beta}{\mathrm{2}}\right)}=\frac{{p}}{{q}} \\ $$$${tan}\left(\alpha+\beta\right)=\frac{{p}}{{q}} \\ $$$$>>>>>>>>>>>>>>>> \\ $$$$ \\ $$