Question

Dado tg x=1/2, calcule o valor de y= tg (x+45°) = tg (x-45°)

Answer 1

Vamos lá:

$y = tg(x + 45) + tg(x - 45) \\\ tg(a + b) = \frac{tg a + tg b}{1 - tg a.tg b} \\\\ tg(a - b) = \frac{tg a - tg b}{1 + tg a.tg b} \\\\ y = \frac{tg x + tg 45}{1 + tg x.tg 45} + \frac{tg x - tg 45}{1 - tg x.tg 45} \\\\ tg x = \frac{1}{2} \\\\ tg 45 = 1 \\\ y = \frac{\frac{1}{2} + 1}{1 - \frac{1}{2}.1} + \frac{\frac{1}{2} - 1}{1 + \frac{1}{2}.1} \\\\ y = \frac{\frac{3}{2}}{\frac{1}{2}} - \frac{\frac{1}{2}}{\frac{3}{2}} \\\\ y = 3 - \frac{1}{3} \\\\ y = \frac{8}{3}$

Espero ter ajudado.