Question

Se a tg a=1/4, Calculando tg 2a teremos? *
1 ponto
A)1
B)2/8
C)2/4
D)15/16
E)8/15

Answer 1

Explicação passo-a-passo:

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

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

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

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

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

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

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

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

Letra E