Question

Sabendo que tg(x+y) = 5/4 e tg x = 2/4, determine o valor de tg (y)

Answer 1

Resposta:

$\tan(x + y) = \frac{ \tan(y) + \tan(x) }{1 - \tan(x) \tan(y) } = \frac{5}{4}$

$\frac{ \frac{2}{4} + \tan(y) }{1 - \frac{2}{4} \tan(y) } = \frac{5}{4}$

$\frac{ \frac{1+2 \tan(y) }{2} }{ \frac{2 - \tan(y)}{2} } = \frac{5}{4}$

$\frac{1 + 2 \tan(y) }{2 - \tan(y) } = \frac{5}{4}$

$4(1 + 2 \tan(y) ) = 5(2 - \tan(y))$

$4 + 8 \tan(y) = 10 - 5 \tan(y)$

$13 \tan( y ) = 6 \: \: \: \: \tan(y) = \frac{6}{13}$