2tg в квадрате x+3tgx-2=0

Question

2tg в квадрате x+3tgx-2=0

Answer 1

2tg^2x + 3tgx - 2 = 0 

tgx = t
2t^2 + 3t - 2 = 0 
D = 9 + 16 = 25
t1 = ( - 3 + 5)/4 = 1/2 = 0,5
t2 = ( - 3  - 5)/4 = - 8/4 = - 2

tgx = 0,5
x = arctg(0,5) + pik, k ∈Z

tgx = - 2 
x = - arctg(2) + pik, k ∈Z