Question Number 62388 by hovea cw last updated on 20/Jun/19
$$\mathrm{If}\:\mathrm{tan}\:\theta=\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{tan}\:\phi=\frac{\mathrm{1}}{\mathrm{3}},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\theta\:+\:\phi\:\:\:\mathrm{is} \\ $$
Commented by Tony Lin last updated on 20/Jun/19
$${tan}\left(\theta+\emptyset\right)=\frac{{tan}\theta+{tan}\emptyset}{\mathrm{1}−{tan}\theta{tan}\phi}=\mathrm{1} \\ $$$$\Rightarrow\theta+\emptyset=\frac{\pi}{\mathrm{4}}+\mathrm{2}{n}\pi\:{or}\:\theta+\emptyset=\frac{\mathrm{5}\pi}{\mathrm{4}}+\mathrm{2}{n}\pi \\ $$
Answered by ajfour last updated on 20/Jun/19
$$\mathrm{tan}\:\left(\theta+\phi\right)=\mathrm{1} \\ $$$$\Rightarrow\:\theta+\phi\:=\:{n}\pi+\pi/\mathrm{4}\:. \\ $$