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if-tan-x-y-3-4-and-tan-x-y-8-15-show-that-tan-2x-77-36-




Question Number 43875 by peter frank last updated on 16/Sep/18
if   tan (x+y)=(3/4)  and tan(x−y)=(8/(15))   show that  tan 2x= ((77)/(36))
$${if}\:\:\:\mathrm{tan}\:\left({x}+{y}\right)=\frac{\mathrm{3}}{\mathrm{4}}\:\:{and}\:\mathrm{tan}\left({x}−{y}\right)=\frac{\mathrm{8}}{\mathrm{15}}\: \\ $$$${show}\:{that}\:\:\mathrm{tan}\:\mathrm{2}{x}=\:\frac{\mathrm{77}}{\mathrm{36}} \\ $$
Answered by ajfour last updated on 16/Sep/18
tan (x+y+x−y)=(((3/4)+(8/(15)))/(1−(2/5)))  ⇒     tan 2x = ((77)/(36)) .
$$\mathrm{tan}\:\left({x}+{y}+{x}−{y}\right)=\frac{\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{8}}{\mathrm{15}}}{\mathrm{1}−\frac{\mathrm{2}}{\mathrm{5}}} \\ $$$$\Rightarrow\:\:\:\:\:\mathrm{tan}\:\mathrm{2}{x}\:=\:\frac{\mathrm{77}}{\mathrm{36}}\:. \\ $$

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