10sin2x + 11sinx - 8 = 0

10*2sin x*cos x + 11sin x - 8 = 0
20 sin x*cos x + 11sin x - 8 = 0
11 sin x (9sin x*cos x + 1) - 8 = 0
 (11 sin x - 8)(9sin x*cos x + 1) = 0
11 sin x - 8 = 0
11 sin x  = 8
sin x = 8/11
x = arcsin 8/11 + 2*пи*k
и
x = -arcsin 8/11 + 2*пи*k
или
9sin x*cos x + 1=0
9sin x*cos x = -1
sin x = -1
x = -пи/2 + 2*пи*k
или
cos x = -1
x=пи + 2*пи*k
ответ: arcsin 8/11 + 2*пи*k ; -arcsin 8/11 + 2*пи*k ; -пи/2 + 2*пи*k ; пи + 2*пи*k