1)2sinx^2-6cosx+6=0 2) cos2x-2sinxcosx-3sin2x=0 3)sin4xcos3x+sin3xcos4x = -1 4) 7sin^2x-4sin2x+cos^2x=0 5) 4sinx-3=3cosx

Найдем корни. 

1) 2 * sin x 6 * cos x + 6 = 0;

2 * (1 - cos x) 6 * cos x + 6 = 0;

-2 * cos x + 2 6 * cos x + 6 = 0;

-2 * cos x 6 * cos x + 8 = 0;

2 * cos x + 6 * cos x 8 = 0;

cos x + 3 * cos x 4 = 0;

D = 9 4 * 1 * (-4) = 9 + 16 = 25 = 5;

1. cos x = (-3 + 5)/2 = 2/2 = 1;

cos x = 1;

x = 2 * pi * n, n Z;

1. cos x = (-3 5)/2 = -8/2 = -4;

Нет корней.

Ответ: x = 2 * pi * n, n Z.

2) cos (2 * x) 2  * sin x * cos x 3 * sin (2 * x) = 0;

cos x - sin x 2 * sin x * cos x 3 * 2 * sin x * cos x = 0;

cos x - sin x 8 * sin x * cos x = 0;

1 tg x 8 * tg x = 0;

tg x + 8 * tg x 1 = 0;

D = 64 4 * 1 * (-1) = 64 + 4 = 70; 

1. tg x = (-8 + 70)/2;

x = arctg ((-8 + 70)/2) + pi * n, n Z;

1. tg x = (-8 - 70)/2;

x = arctg ((-8 - 70)/2) + pi * n, n Z.

3) sin (4 * x) * cos (3 * x) + sin (3 * x) * cos (4 * x) = -1;

sin (4 * x + 3 * x) = -1;

sin (7 * x) = -1;

7 * x = -pi/2 + 2 * pi * n, n Z;

x = -pi/14 + 2 * pi/7 * n, n Z;

4) 7 * sin x 4 * sin (2 * x) + cos x = 0; 

7 * sin x 8 * sin x * cos x + cos x = 0;

7 * tg x 8 * tg x + 1 = 0;

D = 64 4  * 1 * 7 = 64 28 = 36;

1. tg x = (8 + 6)/14 = 1;

x = pi/4 + pi * n, Z;

1. tg x = (8 6)/14 = 1/7;

x = arctg (1/7) + pi * n, n Z;

5) 4 * sin x 3 = 3 * cos x;

16 * sin x 24 * sin x + 9 = 9 * cos x;

16 * sin x 24 * sin x + 9 * sin x + 9 * cos x 9 * cos x = 0;

25 * sin x 24 * sin x = 0;

sin x * (25 * sin x 24) = 0;

1. sin x = 0;

x = pi * n, n Z;

1. 25 * sin x = 24;

sin x = 24/25;

x = (-1)^n * arcsin (24/25) + pi * n, n Z.