Question Number 176812 by mathlove last updated on 27/Sep/22
$${tan}\left({a}−{b}\right)={x}\:\:\:\:{and}\:\:\:{tan}\left({a}+{b}\right)={y} \\ $$$${then}\:\:\:\:{tan}\mathrm{2}\alpha=? \\ $$
Commented by cortano1 last updated on 27/Sep/22
$$\:\mathrm{tan}\:\mathrm{2}{a}=? \\ $$
Answered by cortano1 last updated on 27/Sep/22
$$\:\mathrm{2}{a}=\left({a}+{b}\right)+\left({a}−{b}\right) \\ $$$$\:\mathrm{tan}\:\mathrm{2}{a}=\frac{\mathrm{tan}\:\left({a}+{b}\right)+\mathrm{tan}\:\left({a}−{b}\right)}{\mathrm{1}−\mathrm{tan}\:\left({a}+{b}\right)\:\mathrm{tan}\:\left({a}−{b}\right)} \\ $$$$\:=\:\frac{{x}+{y}}{\mathrm{1}−{xy}}\: \\ $$
Commented by peter frank last updated on 27/Sep/22
$$\mathrm{good} \\ $$
Commented by mathlove last updated on 27/Sep/22
$${thanks} \\ $$