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tan-a-b-1-17-tan-a-b-11-13-tan2a-tan2b-




Question Number 166170 by mathls last updated on 14/Feb/22
tan(a+b)=(1/(17))   ,   tan(a−b)=((11)/(13))  tan2a=?      tan2b=?
$${tan}\left({a}+{b}\right)=\frac{\mathrm{1}}{\mathrm{17}}\:\:\:,\:\:\:{tan}\left({a}−{b}\right)=\frac{\mathrm{11}}{\mathrm{13}} \\ $$$${tan}\mathrm{2}{a}=?\:\:\:\:\:\:{tan}\mathrm{2}{b}=? \\ $$
Answered by cortano1 last updated on 14/Feb/22
⇒2a = (a+b)+(a−b)  ⇒tan 2a =(((1/(17))+((11)/(13)))/(1−(1/(17)).((11)/(13)))) = ((20)/(21))
$$\Rightarrow\mathrm{2}{a}\:=\:\left({a}+{b}\right)+\left({a}−{b}\right) \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{2}{a}\:=\frac{\frac{\mathrm{1}}{\mathrm{17}}+\frac{\mathrm{11}}{\mathrm{13}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{17}}.\frac{\mathrm{11}}{\mathrm{13}}}\:=\:\frac{\mathrm{20}}{\mathrm{21}} \\ $$
Commented by mathls last updated on 14/Feb/22
thanks
$${thanks} \\ $$
Answered by cortano1 last updated on 14/Feb/22
⇒2b=(a+b)−(a−b)  ⇒tan 2b=(((1/(17))−((11)/(13)))/(1+(1/(17)).((11)/(13))))= −(3/4)
$$\Rightarrow\mathrm{2}{b}=\left({a}+{b}\right)−\left({a}−{b}\right) \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{2}{b}=\frac{\frac{\mathrm{1}}{\mathrm{17}}−\frac{\mathrm{11}}{\mathrm{13}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{17}}.\frac{\mathrm{11}}{\mathrm{13}}}=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$

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