A) 4cos^2x/2+0,5sinx+3sin^2x/2=3

b) sin^4x-cos^4x=0,5

А) 4cos² (x/2) + 0,5sinx + 3sin² (x/2) = 3

4cos² (x/2) + 2·0,5sin (x/2) ·cos (x/2) + 3sin² (x/2) = 3sin² (x/2) + 3cos² (x/2)

cos² (x/2) + sin (x/2) cos (x/2) = 0

cos (x/2) [cos (x/2) + sin (x/2) ] = 0

1) cos (x/2) = 0

x/2 = π/2 + πn, n ∈ Z

x = π + 2πn, n ∈ Z

2) cos (x/2) + sin (x/2) = 0

cos (x/2) = - sin (x/2)

tg (x/2) = - 1

x/2 = - π/4 + πk, k ∈ Z

x = - π/2 + 2πk, k ∈ Z

Ответ: x = π + 2πn, n ∈ Z; - π/2 + 2πk, k ∈ Z.

б) sin⁴x - cos⁴x = 0,5

(sin²x - cos²x) (sin²x + cos²x) = 0,5

sin²x - cos²x = 0,5

-cos2x = 1/2

cos2x = - 1/2

2x = ±2π/3 + 2πn, n ∈ Z

x = ±π/3 + πn, n ∈ Z

Ответ: x = ±π/3 + πn, n ∈ Z.