§ 44: 44.63 (1)

44.63 Розв’яжіть рівняння

1) cosx2 + cosx = 0;

cosx2 + cos²x2 – sin²x2 = 0;

cos²x2 + cosx2 – (1 – cos²x2) = 0;

2cos²x2 + cosx2 – 1 = 0;

cosx2 = t;

2t² + t – 1 = 0;

D = 1 + 8 = 9; t1 = –1 + 3 = –1;

cosx2 = 12, або cosx2 = –1;

x2 = ± arccos12 + 2πn, n ∈ Z; x2 = π + 2πn, n ∈ Z;

x2 = ± π3 + 2πn, n ∈ Z; x = 2π + 4πn, n ∈ Z;

x = ± 2π3 + 4πn, n ∈ Z.

2) tgx + ctgx = –2;

tgx + 1tgx + 2 = 0;

tg2x+2tgx+1tg x = 0;

(tg x+1)2tgx = 0;

tg x = –1;

x = –π4 + πn, n ∈ Z.