1) 2cos^2x - 1 - sinx = 0 2) 2sin^2x - 1 + cosx = 0 3) 2cos^2x - 1 + sinx = 0 4) cos2x - cosx = 0 5) sinx + cosx + sin3x = 0 6) 2sin^2x - 5sinxcosx + 5cos^2x = 1 7) sqrt3cosx - sinx = 0 8) sqrt3cosx - sinx = 1 9) sin^2x + cos^2 2x + sin^2 3x = 3/2

Question

Arika

Математика

9 января, 22:38

1) 2cos^2x - 1 - sinx = 0 2) 2sin^2x - 1 + cosx = 0 3) 2cos^2x - 1 + sinx = 0 4) cos2x - cosx = 0 5) sinx + cosx + sin3x = 0 6) 2sin^2x - 5sinxcosx + 5cos^2x = 1 7) sqrt3cosx - sinx = 0 8) sqrt3cosx - sinx = 1 9) sin^2x + cos^2 2x + sin^2 3x = 3/2

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Дамир Козлов · Answer 1

Решим уравнения:

1) 2 * cos^2 x - 1 - sin x = 0;

2 - 2 * sin^2 x - sin x - 1 = 0;

-2 * sin^2 x - sin x + 1 = 0;

2 * sin^2 x + sin x - 1 = 0;

a) sin x = - 1;

x = - pi/2 + 23 * pi * n;

b) sin x = 1/2;

x = (-1) ^n * pi/6 + pi * n;

2) 2 * sin^2 x - 1 + cos x = 0;

2 - 2 * cos^2 x + cos x - 1 = 0;

-2 * cos^2 x + cos x - 1 = 0;

2 * cos^2 x - cos x + 1 = 0;

Нет корней.

3) 2 * cos^2 x - 1 + sinx = 0;

2 - 2 * sin^2 x + sin x - 1 = 0;

-2 * sin^2 x + sin x + 1 = 0;

2 * sin^2 x - sin x - 1 = 0;

a) sin x = - 1/2;

x = (-1) ^n * (-pi/6) + pi * n;

b) sin x = 1;

x = pi/2 + 2 * pi * n;

4) cos (2 * x) - cos x = 0;

cos^2 x - sin^2 x - cos x = 0;

cos^2 x - 1 + cos^2 x - cos x = 0;

2 * cos^2 x - cos x - 1 = 0;

a) cos x = - 1/2;

x = + -2 * pi/3 + 2 * pi * n;

b) cos x = 1;

x = 2 * pi * n;

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

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

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

a) cos x = 1;

x = 2 * pi * n;

b) sin (2 * x) = - 1/2;

2 * x = (-1) ^n * (-pi/6) + pi * n;

x = (-1) ^n * (-pi/12) + pi/2 * n;

6) 2 * sin^2 x - 5 * sin x * cos x + 5 * cos^2 x = 1;

2 * sin^2 x - 5 * sin x * cos x + 5 * cos^2 x - sin^2 x - cos^2 x = 0;

sin^2 x - 5 * sin x * cos x + 4 * cos^2 x = 0;

tg^2 x - 5 * tg x + 4 = 0;

a) tg x = 1;

x = pi/4 + pi * n;

b) tg x = 4;

x = arctg 4 + pi * n;

7) √3 * cos x - sin x = 0;

3 * cos^2 x - 2 * √3 * cos x * sin x + sin^2 x = 0;

tg^2 x - 2 * √3 * tg x + 3 = 0;

(tg x - √3) = 0;

tg x = √3;

x = pi/3 + pi * n;

8) √3 * cos x - sin x = 1;

3 * cos^2 x - 2 * √3 * cos x * sin x + sin^2 x - 1 = 0;

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

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

cos^2 x - √3 * cos x * sin x = 0;

cos x * (cos x - √3 * sin x) = 0;

a) cos x = 0;

x = pi/2 + pi * n;

b) cos^2 x - 2 * √3 * cos x * sin x + 3 * sin^2 x = 0;

3 * tg^2 x - 2 * √3 * tg x + 1 = 0;

(√3 * tg x - 1) ^2 = 0;

tg x = √3/3;

x = pi/6 + pi * n;

9) sin^2 x + cos^2 2x + sin^2 3x = 3/2;

sin^2 x + cos^2 x - sin^2 x - sin^2 (3 * x) = 3/2;

cos^2 x - sin^2 (3 * x) = 3/2;

2 * cos^2 x - 2 * sin^2 (3 * x) = 3;

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

Нет решения.