6Sin²x - 7Sinx - 5 = 0
Sinx = m , - 1 ≤ m ≤ 1
6m² - 7m - 5 = 0
D = (- 7)² - 4 * 6 * (- 5) = 49 + 120 = 169 = 13²
![m_{1} =\frac{7-13}{12}=-\frac{6}{12}=-\frac{1}{2} \\\\m_{2}=\frac{7+13}{12}=\frac{20}{12}=1\frac{2}{3}](https://tex.z-dn.net/?f=m_%7B1%7D+%3D%5Cfrac%7B7-13%7D%7B12%7D%3D-%5Cfrac%7B6%7D%7B12%7D%3D-%5Cfrac%7B1%7D%7B2%7D+%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B7%2B13%7D%7B12%7D%3D%5Cfrac%7B20%7D%7B12%7D%3D1%5Cfrac%7B2%7D%7B3%7D)
Корень m₂ - не подходит так как больше единицы.
![Sinx=-\frac{1}{2}\\\\x=(-1)^{n}arcSin(-\frac{1}{2})+\pi n,n\in Z\\\\x=(-1)^{n+1}arcSin\frac{1}{2}+\pi n,n\in Z\\\\x=(-1)^{n+1}\frac{\pi }{6}+\pi n,n\in Z](https://tex.z-dn.net/?f=Sinx%3D-%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cx%3D%28-1%29%5E%7Bn%7DarcSin%28-%5Cfrac%7B1%7D%7B2%7D%29%2B%5Cpi+n%2Cn%5Cin+Z%5C%5C%5C%5Cx%3D%28-1%29%5E%7Bn%2B1%7DarcSin%5Cfrac%7B1%7D%7B2%7D%2B%5Cpi+n%2Cn%5Cin+Z%5C%5C%5C%5Cx%3D%28-1%29%5E%7Bn%2B1%7D%5Cfrac%7B%5Cpi+%7D%7B6%7D%2B%5Cpi+n%2Cn%5Cin+Z)
А/(а+2в)
2в/(а-2в)
общий знаменатель а²-4в², домножим первое на (а-2в), второе на (а+2в)
а/(а+2в)=(а²-2ав)/а²-4в²
2в/(а-2в)=(2ав+4в²)/(а²-4в²)
Sin(-a)=-sina, cotg a= cosa/sina, cos(360-a)=cos(-a) =cosa,
tg(180+a)=tga=sina/cosa=1/cotga
sin(-a)cotga/cos(360-a)(tg(180+a)=-sina.cotga/cosa.tga=
=-cosa/sina = - cotga