Question

Sa se demonstreze identitatea:
tgα +tgβ + tg Y = tgα tg β tgY , unde α,β.Y sint masurile unghiurilor unui triunghi

Answer 1

$\alpha+\beta+\gamma=\pi\Rightarrow tg(\alpha+\beta+\gamma)=tg\pi=0,\;dar\\\\tg(\alpha+\beta+\gamma)=\dfrac{tg(\alpha+\beta)+tg\gamma}{1-tg(\alpha+\beta)\cdot tg\gamma}=\\\\\\=\dfrac{\dfrac{tg\alpha+tgb}{1-tg\alpha\cdot tgb}+tg\gamma}{1-\dfrac{tg\alpha+tgb}{1-tg\alpha\cdot tgb}\cdot tg\gamma}=\\\\\\=\dfrac{tg\alpha+tgb+tg\gamma-tg\alpha\cdot tgb\cdot tg\gamma}{1-tg\alpha\cdot tgb-tg\alpha\cdot tg\gamma-tgb\cdot tg\gamma}=0.$[tex][/tex]

Din cele de mai sus rezultă exact relaţia din enunţ.

Green eyes.