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Question Number 116009 by Khalmohmmad last updated on 30/Sep/20

$$\{\begin{array}{l}\tan (\mathrm{a}+\mathrm{b})=\mathrm{y}\\ \tan (\mathrm{a}-\mathrm{b})=\mathrm{x}\end{array}\tan 2\mathrm{a}=?$$

Answered by bemath last updated on 30/Sep/20

$$\{\begin{array}{l}a+b=r\\ a-b=s\end{array}\Rightarrow 2a=r+s$$$$\tan \left(2a\right)=\frac{\tan r+\tan s}{1-\tan r.\tan s}$$$$=\frac{x+y}{1-xy}$$

Answered by bobhans last updated on 30/Sep/20

$$2a=(a+b)+(a-b)$$$$\tan \left(2a\right)=\frac{\tan (a+b)+\tan (a-b)}{1-\tan (a+b).\tan (a-b)}$$$$=\frac{y+x}{1-yx}$$

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