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 ((pi/2) - х) = 03) 3 sin x+2cos x=04) 3sin x+4cos x=15) tg x=3ctg x6) 3tg^2 x - корень3 tg x=07) sin 3x=cos 5x

Найдем корни.

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.