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) = 34cos²(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) = 0cos(x/2)[cos(x/2) + sin(x/2)] = 01) cos(x/2) = 0x/2 = π/2 + πn, n ∈ Zx = π + 2πn, n ∈ Z2) cos(x/2) + sin(x/2) = 0cos(x/2) = -sin(x/2)tg(x/2) = -1x/2 = -π/4 + πk, k ∈ Zx = -π/2 + 2πk, k ∈ ZОтвет: x = π + 2πn, n ∈ Z; -π/2 + 2πk, k ∈ Z.б) sin⁴x - cos⁴x = 0,5(sin²x - cos²x)(sin²x + cos²x) = 0,5sin²x - cos²x = 0,5-cos2x = 1/2cos2x = -1/22x = ±2π/3 + 2πn, n ∈ Zx = ±π/3 + πn, n ∈ ZОтвет: x = ±π/3 + πn, n ∈ Z.