Question Number 116975 by ZiYangLee last updated on 08/Oct/20
$$\mathrm{Prove}\:\frac{\mathrm{cos}\left({A}−{B}\right)}{\mathrm{sin}\left({A}+{B}\right)}=\frac{\mathrm{1}+\mathrm{tan}\:{A}\mathrm{tan}\:{B}}{\mathrm{tan}\:{A}\mathrm{tan}\:{B}} \\ $$
Commented by Dwaipayan Shikari last updated on 08/Oct/20
$$\frac{{cos}\left({A}−{B}\right)}{{sin}\left({A}+{B}\right)}=\frac{{cosAcosB}+{sinAsinB}}{{sinAcosB}+{cosAsinB}}=\frac{\mathrm{1}+{tanAtanB}}{{tanA}+{tanB}} \\ $$