Question

решите уравнение tg^2x-3tg x+2=0

Answer 1

tgx=t;
t^2 - 3t + 2 = 0;
t^2 - 2t - t +2 = 0;
t*(t-2) - (t-2) = 0;
(t-2)*(t-1) = 0;
t=2 или t=1;
1) tgx = 2; <=> x=arctg(2)+п*m, m целое.
2) tgx = 1; <=> x=arctg(1) + п*n = (п/4) + п*n, n целое.