1. cos4x=корень из 3/2 2. sinx/2=-корень из 2/2 3. 2sin^2x+sinx-1=0 4. tg (x+П/6) = 1 / корень из 3 5.4tgx+3ctgx=7

1) cos (4x) = √3/2;

4x = arccos (√3/2) + - 2 * π * n, где n - натуральное число;

x = π/24 + - π/2 * n.

2) sin (x/2) = - √2/2;

x/2 = arcsin ( - √2/2) + - 2 * π * n;

x = π/2 + - 4 * π * n;

3) 2sin^2 (x) + sin (x) - 1 = 0;

sin (x) = (-1 + - √1 - 4 * 2 * (-1)) / 4 = (-1 + - 3) / 2;

sin (x) = 1; sin (x) = - 2 - уравнение корней не имеет;

x = π/2 + - 2 * π * n.

4) tg (x + π/6) = 1/√3;

x + π/6 = arctg (1/√3) + - π * n;

x = + - π * n;

5)

4tg (x) + 3ctg (x) = 4 + 3;

4 (tg (x) - 1) = 3 (1 - ctg (x));

tg (x) = 3/4.

x = arctg (3/4)