1) sin (x/3 - pi) = √3/22) √2cos x/4 - 1 = 03) tg (x/2 + pi/3) - √3 = 04) 3ctc 3x = - √35) y = 8/ctg x + 1

1) sin (x/3 - π) = √3/2;

x/3 - π = arcsin (√3/2) + - 2 * π * n, где n - натуральное число;

x/3 = π/3 + π + - 2 * π * n;

x = π + 3π + - 6 * π * n;

x = 4π + - 6 * π * n.

2) √2cos (x/4) - 1 = 0;

cos (x/4) = 1/√2;

x/4 = arccos (1/√2) + - 2 * π * n, где n - натуральное число;

x/4 = π/4 + - 2 * π * n;

x = π + - 8 * π * n.

3) tg (x/2 + π/3) - √3 = 0;

tg (x/2 + π/3) = √3;

x/2 + π/3 = arctg (√3) + - π * n, где n - натуральное число;

x/2 + π/3 = π/3 + - π * n;

x = + - 2 * π * n.

4) 3ctg (3x) = - √3;

3x = arcctg (-√3/3) + - π * n.