Sqrt (3) * cos ((pi/3) + x) + 3/2sinx=sqrt (3) / 2

Cos (π/3 + x) = Cosπ/3 Cosx - Sinπ/3 Sinx = 1/2*Cosx - √3/2*Sinx

теперь наше уравнение:

√3 (1/2*Cosx - √3/2*Sinx) = √3/2

√3/2Cosx - 3/2Sinx = √3/2 |*2

√3 Сosx - 3Sinx = √3

√3 Сosx - 3Sinx = √3*1

√3 (Cos²x/2 - Sin²x/2) - 6Sinx/2Cosx/2=√3 (Cos²x/2 + Sin²x/2)

√3Cos²x/2 - √3Sin²x/2 - 6Sinx/2Cosx/2=√3Cos²x/2 + √3Sin²x/2

2√3Sinx/2 + 6Sinx/2Cosx/2 = 0

Sinx/2 (2√3 + 6Cosx/2) = 0

Sinx/2 = 0 или 2√3 + 6 Сosx/2 = 0

x/2 = πk, k ∈Z Cosx/2 = - √3/3

x = 2πk, k ∈Z x/2 = + - arcCos (-√3/3) + 2πn, n∈Z

x = + - 2arcCos (-√3/3) + 4πn, n ∈Z