Question

se tg ( x + \pi / 4) = 3 então tg 2x é igual a:

Answer 1

$3=tg(x+ \pi /4)= \frac{tg(x)+tg(\pi/4)}{1-tg(x)tg(\pi/4)} = \frac{tg(x)+1}{1-tg(x)} 3-3tg(x)=tg(x)+1 4tg(x)=2 tg(x)=1/2$


logo tg(2x)=2tg(x)/(1-tg(x)^2)=1/[1-1/4]=1/3/4=4/3.