Держи с: Удачи с заданием
<span>sin3a+sin6a+sin9a=sin9a+sin9a+sin18a</span>
-2х2+3х+5=3
-2х2+3х+5-3=0
-2х2+3х+2=0 / * -1
2х2 - 3х - 2 = 0
Далее находишь два корня через дискриминант.
А) Выносим общий множитель за скобки (x-3):
5(x-3)-4x(x-3)
(5-4x)(x-3)
Б) (15+a)(b-2)-(2a+3)(2-b)
Сначала перемножаем скобки: 15b - 30 + ab - 2a - (4a -2ab -6 +3b)
Т.к. перед скобками есть знак "-", то знаки всех членов в скобках заменяются на противоположные:
15b - 30 + ab - 2a - 4a + 2ab + 6 - 3b
Приводим подобные и вычисляем:
12b - 24 +3ab - 6a - упрощено
a)
![\sin(\alpha) = \sqrt{1 - \cos^2(\alpha)} = -\frac{4}{5}\\\sin(\pi/3 - \alpha) = \sin(\pi/3)\cos(\alpha) - \cos(\pi/3)\sin(\alpha) = -\frac{3\sqrt{3}}{10} + \frac{2}{5}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%29+%3D+%5Csqrt%7B1+-+%5Ccos%5E2%28%5Calpha%29%7D+%3D+-%5Cfrac%7B4%7D%7B5%7D%5C%5C%5Csin%28%5Cpi%2F3+-+%5Calpha%29+%3D+%5Csin%28%5Cpi%2F3%29%5Ccos%28%5Calpha%29+-+%5Ccos%28%5Cpi%2F3%29%5Csin%28%5Calpha%29+%3D+-%5Cfrac%7B3%5Csqrt%7B3%7D%7D%7B10%7D+%2B+%5Cfrac%7B2%7D%7B5%7D)
б)
![\cos(\beta) = \sqrt{1 - \sin^2(\beta)} = \frac{8}{17}\\\cos(\pi/6 + \beta) = \cos(\beta)\cos(\pi/6) - \sin(\beta)\sin(\pi/6) = \frac{4\sqrt{3}}{17} + \frac{15}{34}](https://tex.z-dn.net/?f=%5Ccos%28%5Cbeta%29+%3D+%5Csqrt%7B1+-+%5Csin%5E2%28%5Cbeta%29%7D+%3D+%5Cfrac%7B8%7D%7B17%7D%5C%5C%5Ccos%28%5Cpi%2F6+%2B+%5Cbeta%29+%3D+%5Ccos%28%5Cbeta%29%5Ccos%28%5Cpi%2F6%29+-+%5Csin%28%5Cbeta%29%5Csin%28%5Cpi%2F6%29+%3D+%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B17%7D+%2B+%5Cfrac%7B15%7D%7B34%7D)
в)
![tg(\pi/4 + \alpha) = \frac{tg(\pi/4) + tg(\alpha)}{1 - tg(\pi/4)tg(\alpha)} = \frac{1 + tg(\alpha)}{1 - tg(\alpha)} = 2](https://tex.z-dn.net/?f=tg%28%5Cpi%2F4+%2B+%5Calpha%29+%3D+%5Cfrac%7Btg%28%5Cpi%2F4%29+%2B+tg%28%5Calpha%29%7D%7B1+-+tg%28%5Cpi%2F4%29tg%28%5Calpha%29%7D+%3D+%5Cfrac%7B1+%2B+tg%28%5Calpha%29%7D%7B1+-+tg%28%5Calpha%29%7D+%3D+2)
г)
Тут ошибка в условии, ведь
.
д)
![\pi / 2 < \alpha, \beta < \pi](https://tex.z-dn.net/?f=%5Cpi+%2F+2+%3C+%5Calpha%2C+%5Cbeta+%3C+%5Cpi)
![\cos(\alpha) = -0.8, \cos(\beta) = -0.6\\\sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta) = 0.28\\\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) = 0](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%29+%3D+-0.8%2C+%5Ccos%28%5Cbeta%29+%3D+-0.6%5C%5C%5Csin%28%5Calpha+-+%5Cbeta%29+%3D+%5Csin%28%5Calpha%29%5Ccos%28%5Cbeta%29+-+%5Ccos%28%5Calpha%29%5Csin%28%5Cbeta%29+%3D+0.28%5C%5C%5Ccos%28%5Calpha+%2B+%5Cbeta%29+%3D+%5Ccos%28%5Calpha%29%5Ccos%28%5Cbeta%29+-+%5Csin%28%5Calpha%29%5Csin%28%5Cbeta%29+%3D+0)