Решите тригометрическое уравнение 15 (1+sinx) во второй степени=17+31sinx

15 (sinx + 1) ^2 = 17 + 31sinx

15 (sin^2x + 2sinx + 1) = 17 + 31sinx

15sin^2x + 30sinx + 15 = 17 + 31sinx

15sin^2x + 30sinx + 15 - 17 - 31sinx = 0

15sin^2x - sinx - 2 = 0

sinx=t, t ∈ [ - 1; 1]

15t^2 - t - 2 = 0

D = 1 + 4*30 = 121

t1 = (1 + 11) / 30 = 12/30 = 2/5

t2 = (1 - 11) / 30 = - 10/30 = - 1/3

sinx = 2/5

x = (-1) ^k arcsin (2/5) + pik. k ∈Z

sinx = - 1/3

x = (-1) ^ (k+1) arcsin (1/3) + pik. k ∈Z