1)6x(x-y)-8(x-y)=(6x-8)(x-y)
2)a(a-b)-5(a-b)=(a-5)(a-b)
3)b(b+c)+a(b+c)=(b+a)(b+c)
4)xy(3-(x^2)*(y^2))-2(3-(x^2)*(y^2))=(xy-2)*(3-(x^2)(y^2)
Cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b)
cos²a+sin²a=1
sin²a=1-cos²a
sina = +-√(1-cos²a)
Угол a∈(3pi/2;2pi), а это 4 четверть и sin в ней принимает отрицательные значения.
![sina=-\sqrt{1-cos^2a}=-\sqrt{\frac{25}{25}-\frac{16}{25}}=-\sqrt{\frac{9}{25}}=-\frac{3}{5}](https://tex.z-dn.net/?f=sina%3D-%5Csqrt%7B1-cos%5E2a%7D%3D-%5Csqrt%7B%5Cfrac%7B25%7D%7B25%7D-%5Cfrac%7B16%7D%7B25%7D%7D%3D-%5Csqrt%7B%5Cfrac%7B9%7D%7B25%7D%7D%3D-%5Cfrac%7B3%7D%7B5%7D)
Итого:
![cos(a+\frac{\pi}{6})=cos(a)cos(\frac{\pi}{6})-sin(a)sin(\frac{\pi}{6})=\frac{4}{5}*\frac{\sqrt{3}}{2}-(-\frac{3}{5})*\frac{1}{2}=\\=\frac{4\sqrt{3}}{10}+\frac{3}{10}=\frac{4\sqrt{3}+3}{10}](https://tex.z-dn.net/?f=cos%28a%2B%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3Dcos%28a%29cos%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29-sin%28a%29sin%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%5Cfrac%7B4%7D%7B5%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D-%28-%5Cfrac%7B3%7D%7B5%7D%29%2A%5Cfrac%7B1%7D%7B2%7D%3D%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B10%7D%2B%5Cfrac%7B3%7D%7B10%7D%3D%5Cfrac%7B4%5Csqrt%7B3%7D%2B3%7D%7B10%7D)
X+2-3x2-6x=0
-3x2-5x+2=0
D= 25-4*(-3)*2=25+24=49=7^2
x=5+7/-6=-2
x=5-7/-6=одна третья