Cosx = cos^2(x/2) - sin^2(x/2)
sinx = 2*sin(x/2)*cos(x/2)
√3*cos^2(x/2) - √3*sin^2(x/2) + 2*sin(x/2)*cos(x/2) - cos^2(x/2) - sin^2(x/2) = 0
cos^2(x/2)*(√3 - 1) - sin^2(x/2)*(√3 + 1) + 2*sin(x/2)*cos(x/2) = 0 - разделим на cos^2(x/2), получаем:
(√3 - 1) - tg^(x/2)*(√3 + 1) + 2tg(x/2) = 0
Замена: tg(x/2) = t
(√3 + 1)*t^2 - 2t - (√3 - 1) = 0
D = 4 + 4*(√3 - 1)(√3 + 1) = 4 + 4*(3 - 1) = 4 + 4*2 = 12
t1 = (2 - 2√3)/2*(√3 + 1) = (1 - √3) / (1 + √3) = -(1 - √3)^2 / 2 = -(1 - 2√3 + 3)/2 = (2√3 - 4)/2 = √3 - 2
t2 = 1
1) tg(x/2) = 1, (x/2) = π/4 + πk, x = π/2 + 2πk
2) tg(x/2) = √3 - 2, (x/2) = arctg(√3 - 2) + πk, x = 2arctg(√3 - 2) + 2πk
P.S. не уверенна со вторым значением х...