Question

Se tan x = 1/4 , calcule o valor de tan 2x.

Answer 1

1/4= 0,25
x= invtang0,25=14°

2x= 28°

tang(28°)=0,53 aproximadamente 1/2

Answer 2

$\sf tg~(2x)=\dfrac{2\cdot tg~x}{1-tg^2~x}$

$\sf tg~(2x)=\dfrac{2\cdot\frac{1}{4}}{1-\Big(\frac{1}{4}\Big)^2}$

$\sf tg~(2x)=\dfrac{\frac{2}{4}}{1-\frac{1}{16}}$

$\sf tg~(2x)=\dfrac{\frac{1}{2}}{\frac{16-1}{16}}$

$\sf tg~(2x)=\dfrac{\frac{1}{2}}{\frac{15}{16}}$

$\sf tg~(2x)=\dfrac{1}{2}\cdot\dfrac{16}{15}$

$\sf tg~(2x)=\dfrac{16}{30}$

$\sf \red{tg~(2x)=\dfrac{8}{15}}$