Question

Se tg(x + y) = 33e tgx = 3, determine o
valor de tg2y .

Answer 1

tg(x+y) = $\frac{tgx + tgy}{1-tgx.tgy}$

tg(x+y) = $\frac{3+tgy}{1-3tgy}$

33 = $\frac{3+tgy}{1-3tgy}$

33.(1-3tgy) = 3+tgy

33 - 99tgy = 3+tgy

100tgy = 30

tgy = 0,3 .

Calculando tg(2y) :

tg(2y) = tg(y+y)

tg(y+y) = $\frac{tgy+tgy}{1-tgy.tgy}$

tg(2y) = $\frac{2tgy}{1- tg^{2}y }$

tg(2y) = $\frac{2.0,3}{1- 0,3.0,3}$ 

tg(2y) = $\frac{0,6}{1-0,09}$ 

tg(2y) = 0,6/0,91 = 60/91 ou aproximadamente 2/3