Question

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

Answer 1

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

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

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

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

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

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

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

Ответ: $-dfrac{3sqrt{3}}{7}$