Х≠0
х≠1
...................................
Х2+6х-7х-42=0
х2-х-42=0
Д=1-4(-42)=169
х1= 1-13/2=-6
х2=1+13/2=7
1. a²-b²=(a+b)*(a-b) разность квадратов
2. cos²α-sin²α=cos2α косинус двойного аргумента
2. sin²α+cos²α=1 - основное тригонометрическое тождество
![cos^{4} \frac{ \pi }{12}- sin^{4} \frac{ \pi }{12} = ( cos^{2} \frac{ \pi }{12} )^{2} - ( sin^{2} \frac{ \pi }{12} )^{2} =](https://tex.z-dn.net/?f=+cos%5E%7B4%7D+%5Cfrac%7B+%5Cpi+%7D%7B12%7D-+sin%5E%7B4%7D++++%5Cfrac%7B+%5Cpi+%7D%7B12%7D+%3D+%28+cos%5E%7B2%7D+%5Cfrac%7B+%5Cpi+%7D%7B12%7D++%29%5E%7B2%7D+-+%28+sin%5E%7B2%7D++%5Cfrac%7B+%5Cpi+%7D%7B12%7D+%29%5E%7B2%7D+%3D)
![=( cos^{2} \frac{ \pi }{12} + sin^{2} \frac{ \pi }{12} )*( cos^{2} \frac{ \pi }{12} - sin^{2} \frac{ \pi }{12} )=1*cos(2* \frac{ \pi }{2} )=cos \frac{ \pi }{6} = \frac{ \sqrt{3} }{2}](https://tex.z-dn.net/?f=%3D%28+cos%5E%7B2%7D+%5Cfrac%7B+%5Cpi+%7D%7B12%7D+%2B+sin%5E%7B2%7D++%5Cfrac%7B+%5Cpi+%7D%7B12%7D++%29%2A%28+cos%5E%7B2%7D+%5Cfrac%7B+%5Cpi+%7D%7B12%7D+-+sin%5E%7B2%7D++%5Cfrac%7B+%5Cpi+%7D%7B12%7D++%29%3D1%2Acos%282%2A+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%29%3Dcos+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%3D+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D+)
sinx-√3*cosx=0 | : cosx≠0
![\frac{sinx}{cosx}- \frac{ \sqrt{3}*cosx }{cosx}=0](https://tex.z-dn.net/?f=+%5Cfrac%7Bsinx%7D%7Bcosx%7D-+%5Cfrac%7B+%5Csqrt%7B3%7D%2Acosx+%7D%7Bcosx%7D%3D0++)
tgx-√3=0
tgx=√3
![x=arctg \sqrt{3} + \pi n,](https://tex.z-dn.net/?f=x%3Darctg+%5Csqrt%7B3%7D+%2B+%5Cpi+n%2C+)
n∈Z
![x= \frac{ \pi }{3} + \pi n,](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B+%5Cpi+%7D%7B3%7D+%2B+%5Cpi+n%2C+)