Question

найти tga, если tg(a+п/3)=кореньиз3/4​

Answer 1

$\mathrm{tg}\left(\alpha +\dfrac{\pi}{3}\right)=\dfrac{\sqrt{3}}{4}$

$\dfrac{\mathrm{tg}\alpha+\mathrm{tg}\dfrac{\pi}{3} }{1-\mathrm{tg}\alpha\cdot\mathrm{tg}\dfrac{\pi}{3}} =\dfrac{\sqrt{3}}{4}$

$\dfrac{\mathrm{tg}\alpha+\sqrt{3}}{1-\sqrt{3}\mathrm{tg}\alpha} =\dfrac{\sqrt{3}}{4}$

$4(\mathrm{tg}\alpha+\sqrt{3})=\sqrt{3}(1-\sqrt{3}\mathrm{tg}\alpha)$

$4\mathrm{tg}\alpha+4\sqrt{3}=\sqrt{3}-3\mathrm{tg}\alpha$

$7\mathrm{tg}\alpha=-3\sqrt{3}$

$\mathrm{tg}\alpha=-\dfrac{3\sqrt{3}}{7}$

Ответ: $-\dfrac{3\sqrt{3}}{7}$