3sinx + cosx = 3
6sin(0.5x) ·cos(0.5x) + 1 - 2sin²(0.5x) = 3
6sin(0.5x) ·cos(0.5x) - 2sin²(0.5x) = 2
2sin²(0.5x) - 6sin(0.5x) ·cos(0.5x) + 2 = 0
Cos 0.5x ≠ 0
Делим на 2cos²(0.5x)
tg²(0.5x) - 3tg(0.5x) + 1 = 0
Замена: t = tg(0.5x)
t² - 3t + 1 = 0
D = 9 - 4 = 5
t1 = (3 - √5)/2; tg(0.5x) = (3 - √5)/2; 0.5x = arc tg (3 - √5)/2 + πk
x1 = 2arc tg (3 - √5)/2 + 2πk (k∈Z)
t2 = (3 + √5)/2; tg(0.5x) = (3 + √5)/2; 0.5x = arc tg (3 + √5)/2 + πk
x2 = 2arc tg (3 + √5)/2 + 2πk (k∈Z)