§ 29: 29.5

29.5 Розв’яжіть рівняння:

1) tg(3x – π12) = 33; 3x – π12 = arctg33 + πn, n ∈ Z; 3x = π6 + π12 + πn, n ∈ Z; 3x = π4 + πn, n ∈ Z; x = π12 + πn3, n ∈ Z;

2) tg(3 – 2x) = 2; tg(2x – 3) = –2; 2x – 3 = arctg(–2) + πn, n ∈ Z;

2x = arctg(–2) + 3 + πn, n ∈ Z;

x = 12arctg(–2) + 1,5 + πn2, n ∈ Z; x = –12arctg2 + 1,5 + πn2, n ∈ Z.

3) 3ctg (5x + π3) + 3 = 0; ctg (5x + π3) = –3; tg(5x + π3) = –33;

5x + π3 = arctg(–33) + πn, n ∈ Z; 5x = – π6 – π3 + πn, n ∈ Z; 5x = –π2 + πn, n ∈ Z; x = – π10 + πn5, n ∈ Z;

4) ctg(π4 – x3) = 33; tg(x3 – π4) = –3; x3 – π4 = arctg(–3) + πn, n ∈ Z;

x3 = –π3 + π4 + πn, n ∈ Z; x = –π + 3π4 + 3πn, n ∈ Z; x = –π4 + 3πn,

n ∈ Z.