1) 3cos2x+10sin^2x-6=0

2) 5sin 2x-11sin^2 x+3=0 помогите решить

3) 3cos x+19sin x-9=0

1) cos 2x = 1 - 2sin^2 x

3cos 2x + 10sin^2 x - 6 = 3 - 6sin^2 x + 10sin^2 x - 6 = 4sin^2 x - 3 = 0

sin^2 x = 3/4

sin x1 = - √3/2

sin x2 = √3/2

Оба уравнения элементарны.

2) sin 2x = 2sin x*cos x

5sin 2x - 11sin^2 x + 3 = 10sin x*cos x - 11sin^2 x + 3sin^2 x + 3cos^2 x = 0

-8sin^2 x + 10sin x*cos x + 3cos^2 x = 0

Делим все на - cos^2 x

8tg^2 x - 10tg x - 3 = 0

D/4 = 5^2 - 8 (-3) = 25 + 24 = 49 = 7^2

tg x1 = (5 - 7) / 8 = - 1/4

tg x2 = (5 + 7) / 8 = 3/2

Оба уравнения элементарны

3) Переходим к половинным аргументам

3cos^2 (x/2) - 3sin^2 (x/2) + 19*2sin (x/2) * cos (x/2) - 9sin^2 (x/2) - 9cos^2 (x/2) = 0

-12sin^2 (x/2) + 38sin (x/2) * cos (x/2) - 6cos^2 (x/2) = 0

Делим все на - 2cos^2 (x/2)

6tg^2 (x/2) - 19tg (x/2) + 3 = 0

D = 19^2 - 4*6*3 = 361 - 72 = 289 = 17^2

tg (x1/2) = (19 - 17) / 12 = 1/6

tg (x2/2) = (19 + 17) / 12 = 3

Оба уравнения элементарны