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