Question

Calculati tg2x , stiind ca ctg x=3

Answer 1

 

$\displaystyle\bf\\Se~da\!:~~ctg~x=3\\\\Se~cere\!:~~tg~2x\\\\\\Pasul~1:~~Calculam~ctg~2x\\\\ctg~2x=\frac{ctg^2x-1}{2ctg~x}=\frac{3^2-1}{2\times3}=\frac{9-1}{2\times3} =\frac{8}{6}=\boxed{\bf\frac{4}{3}}\\\\Pasul~1:~~Calculam~tg~2x\\\\tg~2x=\frac{1}{ctg~2x}=\frac{~~~1~~~}{\dfrac{4}{3}}=\boxed{\boxed{\bf\frac{3}{4}}}$