1). корень из 3tg (x/3+П/6) = 32). sin2x=корень из2/23) 4 sin в квадратех+11sinx-3=0

1) √3tg (x/3 + π/6) = 3;

tg (x/3 + π/6) = 3/√3; tg (x/3 + π/6) = √3; x/3 + π/6 = π/3 + πk, k ∈ Z; x + π/2 = π + 3πk, k ∈ Z; x = π/2 + 3πk, k ∈ Z.

2) sin2x = √2/2;

2x = π/2 ± π/4 + 2πk, k ∈ Z; x = π/4 ± π/8 + πk, k ∈ Z.

3) 4sin^2 х + 11sinx - 3 = 0;

D = 11^2 + 4 * 4 * 3 = 121 + 48 = 169 = 13^2; sinx = (-11 ± 13) / 8;

a) sinx = (-11 - 13) / 8 = - 24/8 = - 3 < - 1 - нет решений;

b) sinx = (-11 + 13) / 8 = 2/8 = 1/4;

[x = arcsin (1/4) + 2πk, k ∈ Z;

[x = π - arcsin (1/4) + 2πk, k ∈ Z.

Ответ:

1) π/2 + 3πk, k ∈ Z; 2) π/4 ± π/8 + πk, k ∈ Z; 3) arcsin (1/4) + 2πk; π - arcsin (1/4) + 2πk, k ∈ Z.