1) 2sin^2x+sin x-3=02) cos^2(pi-x)-sin ((pi/2)-х)=03) 3 sin x+2cos1) 2sin^2x+sin x-3=02) cos^2(pi-x)-sin

Найдем корешки.

1) 2 * sin^2 x + sin x 3 = 0;

D = 1 4 * 2 * (-3) = 25;

sin x = (-1 + 5)/4 = -1;

sin x = (-1 5)/4 = -3/2.

Найдем х. 

sin x = -1;

x = -пи/2 + 2 * пи * n, n Z.

2) cos^2 (pi - x) - sin ((pi/2) - х) = 0;

cos^2 x cos x = 0;

cos x * (cos x 1) = 0;

cos x = 0;

cos x = 1;

x = пи/2 + пи * n, n Z;

x = 2 * пи * n, n Z.

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

9 * sin^2 x + 12 * sin x * cos x + 4 * cos^2 x = 0;

9 * tg^2 x + 12 * tg x + 4 = 0;

(tg x + 2)^2 = 0;

tg x = -2;

x = arctg (-2) +  пи * n, n Z.

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

9 * sin^2 x + 24 * sin x * cos x + 16 * cos^2 x sin^2 x cos^2 x = 0;

8 * sin^2 x + 24 * sin x * cos x + 15 * cos^2 x = 0;

8 * tg^2 x + 24 * tg x + 15 = 0;

D = 576 4 * 8 * 15 = 96;

tg x = (-24 + 96^0.5)/16;

x = arctg ((-24 + 96^0.5)/16) + пи * n, n Z;

tg x = (-24 - 96^0.5)/16;

x = arctg ((-24 - 96^0.5)/16) + пи * n, n Z. 

5) tg x = 3 * ctg x; 

tg x 3 * ctg x = 0;

tg x 3 * 1/tg x = 0;

tg x не равен 0.

tg^2 x 3 = 0;

tg x = +-3;

x = пи/3 + пи * n, n Z;

x = -пи/6 + пи * n, n Z;

6) 3 * tg^2 x -  3 tg x = 0; 

tg x * (3 * tg x - 3) = 0;

tg x = 0;

tg x = 3/3;

x = пи * n, n Z;

x = пи/6 + пи * n, n Z;

7) sin (3 * x) = cos (5 * x);

sin (3 * x) cos (5 * x) = 0;

Нет корней.