V3 cos x + sin x = 1

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 ...