Question

Sabendo que tgx=5, calcule tg 3x. (Use; 3x=2x + x)

Answer 1

Sabemos que:

tg (a + b) = (tg a + tg b)/(1 - tg a.tg b)
tg (2a) = 2.tg a/(1 - tg² a)

Logo:

tg (2x) = 2.tg x/(1 - tg²x)
tg (2x) = 2.5/(1 - 5²)
tg (2x) = 10/(-24)
tg (2x) = -5/12

tg (2x + x) = (tg 2x + tg x)/(1 - tg 2x.tg x)
tg (3x) = (-5/12 + 5)/(1 - (-5/12).5)
tg (3x) = (55/12)/(1 + 25/12)
tg (3x) = (55/12)/(37/12)
tg (3x) = (55/12).(12/37)
tg (3x) = 55/37

Portanto, tg (3x) = 55/37.