Question

$sqrt{3}$ cos 5x - sin 5x = $-sqrt{3}$

Answer 1

Разделим обе части на 2, получим
√3/2Cos5x - 1/2Sin5x = - √3/2
СosП/6Cos5x - SinП/6Sinx = - √3/2
Сos(П/6 + 5x) = - √3/2
П/6 + 5x = + - 5П/6 + 2Пn, n э z
П/6 + 5x = 5П/6 + 2Пn, n э z                            П/6 + 5x = - 5П/6 + 2Пn,nэ z
5x = 2П/3 + 2Пn, n э z                                       5x = - П + 2Пn, n э z
x = 2П/15 + 2Пn/5, n э z                                        x = - П/5 + 2Пn/5, n э z