Question

se tgα=1/4 e α+β=45°. Calcule tgβ

Answer 1

$tg\alpha =\frac{1}{4}$

$\alpha +\beta = 45\\ \\ \alpha = 45-\beta$

tg45= 1

$tg(45-\beta) = \frac{tg45+tg\beta }{1+tg45.tgt\beta } \\ \\tg(45-\beta) =\frac{1-tg\beta}{1+tg\beta } \\ \\tg (45-\beta ) = tg\alpha = 0,25\\ \\ 0,25+0,25tg\beta = 1- tg\beta \\ \\ 1,25tg\beta = 0,75 \\ \\ tg\beta = 0,6$