√3*sinx + cosx = -√3 (делим обе стороны равенства на 2)

√3/2*sinx + 1/2*cosx = -√3/2

√3/2 = sin(π/3), 1/2 = cos(π/3)

sin(π/3)*sinx + cos(π/3)*cosx = -√3/2

cos(α = β) = sinα*sinβ + cosα*cosβ ⇒

cos(x - π/3) = -√3/2

x - π/3 = +/- 2*π/3 + 2*π*k ⇒

x = π + 2*π*k; x = -π/3 + 2*π*k