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Question Number 107932 by bemath last updated on 13/Aug/20

$$\frac{\mathbb{B}e\mathbb{M}ath}{\bullet }$$$$Given\{\begin{array}{l}\tan (x-y)=\frac{3}{4}\\ \tan x=2\end{array}$$$$find\tan y?$$

Commented by mnjuly1970 last updated on 13/Aug/20

$$excellent.$$

Commented by mr W last updated on 13/Aug/20

$$\tan (x-y)=\frac{\tan x-\tan y}{1+\tan x\tan y}=\frac{3}{4}$$$$\frac{2-\tan y}{1+2\tan y}=\frac{3}{4}$$$$10\tan y=5$$$$\Rightarrow \tan y=\frac{1}{2}$$

Commented by bemath last updated on 13/Aug/20

$$santuyy....$$

Answered by bemath last updated on 13/Aug/20

$$\frac{\mathcal{B}e\mathcal{M}ath}{°\bullet °}$$$$y=x-(x-y)$$$$\tan y=\tan (x-(x-y))$$$$\tan y=\frac{\tan x-\tan (x-y)}{1+\tan x\tan (x-y)}$$$$\tan y=\frac{2-\frac{3}{4}}{1+2\left(\frac{3}{4}\right)}=\frac{\frac{5}{4}}{\frac{10}{4}}=0.5$$

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