1) cos2x=1/2 2) sinx/3=3/2 3) tgx/2=3 4) ctg3x=3/3 5) 4sinx+3=0 6)

1) cos 2 x = 1/2;  

2 x = pi/3 +2 pi k;

x = pi/6 + pi k.

2) sin x/3 = 3/2;

x₁/3 = pi/3 + 2 pi k; x₁ = pi +6 pi k = pi (1 + 6 k);

x₂/3 = pi - pi/3 +2 pi k; x₂ = 3 pi - pi + 6 pi k = 2 pi ( 1+3 k).

3) tg x/2 = 3;

x/2 = pi/3 + pi k;

x = 2 pi/3 + 2 pi k.

4) ctg 3 x = 3/3;

3 x = pi/6 + pi k;

x = pi/18 + pi/3 k.

5) 4 sin x + 3 = 0;

sin x = - 3/4;

x₁ = - arcsin 3/4 + 2 pi k;

x₂ = pi + arcsin 3/4 + 2 pi k;

6) 7 cos x - 2 = 0;

cos x = 2/7;

x = arcos 2/7 + 2 pi k.

7) tg 3 x + 10 = 0;

tg 3 x  = -10;

3 x = - arctg 10 + pi k;

x = - (arctg 10)/3 + pi/3 k. 

8) 12 ctg 2 x = 5;

2 x = arcctg 5/12 + pi k;

x = (arcctg 5/12)/2 + pi/2 k.