Question

Решить тригонометрические уравнения 1. (ctgx+1) * (1-cosx)=0
2. 3 sinx - sin^2x=0
3. cos^2x = 1

Answer 1

1.

$(ctgx + 1)(1 - \cos(x)) = 0 \\ \\ ctgx + 1 = 0 \\ ctgx = - 1 \\ x_1 = - \frac{\pi}{4} + \pi \: n \\ \\ 1 - \cos(x) = 0 \\ \cos(x) = 1 \\ x_2 = 2\pi \: n$

2.

$3 \sin(x) - \sin {}^{2} (x) = 0 \\ \sin(x) (3 - \sin(x)) = 0 \\ \\ \sin(x) = 0 \\ x = \pi \: n \\ \\ 3 - \sin(x) = 0 \\ \sin(x) = 3$

нет корней

3.

$\cos {}^{2} (x) = 1 \\ \cos(x) = \pm1 \\ x = \pi \: n$

везде n принадлежит Z.