((5 корень из 2 в квадрате) - 36) + 6 =
(25*2) - 30 = 20.
13.
![cos2x=sin( \frac{7 \pi }{2}+x ) \\ \\ cos2x=sin( \frac{8 \pi }{2}- \frac{ \pi }{2}+x) \\ \\ cos2x=sin(4 \pi -( \frac{ \pi }{2} )-x) \\ \\ cos2x=-sin( \frac{ \pi }{2}-x ) \\ \\ cos^2x-sin^2x=-cosx \\ cos^2x-(1-cos^2x)+cosx=0 \\ 2cos^2x+cosx-1=0](https://tex.z-dn.net/?f=cos2x%3Dsin%28+%5Cfrac%7B7+%5Cpi+%7D%7B2%7D%2Bx+%29+%5C%5C++%5C%5C+%0Acos2x%3Dsin%28+%5Cfrac%7B8+%5Cpi+%7D%7B2%7D-+%5Cfrac%7B+%5Cpi+%7D%7B2%7D%2Bx%29+%5C%5C++%5C%5C+%0Acos2x%3Dsin%284+%5Cpi+-%28+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%29-x%29+%5C%5C++%5C%5C+%0Acos2x%3D-sin%28+%5Cfrac%7B+%5Cpi+%7D%7B2%7D-x+%29+%5C%5C++%5C%5C+%0Acos%5E2x-sin%5E2x%3D-cosx+%5C%5C+%0Acos%5E2x-%281-cos%5E2x%29%2Bcosx%3D0+%5C%5C+%0A2cos%5E2x%2Bcosx-1%3D0)
![y=cosx \\ \\ 2y^2+y-1=0 \\ D=1+8=9 \\ \\ y_{1}= \frac{-1-3}{4}=-1 \\ \\ y_{2}= \frac{-1+3}{4}= \frac{1}{2}](https://tex.z-dn.net/?f=y%3Dcosx+%5C%5C++%5C%5C+%0A2y%5E2%2By-1%3D0+%5C%5C+%0AD%3D1%2B8%3D9+%5C%5C++%5C%5C+%0Ay_%7B1%7D%3D+%5Cfrac%7B-1-3%7D%7B4%7D%3D-1+%5C%5C++%5C%5C+%0Ay_%7B2%7D%3D+%5Cfrac%7B-1%2B3%7D%7B4%7D%3D+%5Cfrac%7B1%7D%7B2%7D+++)
a) При у= -1
cosx= -1
x=π+2πk, k∈Z
При к=2 x=π+2π*2=5π
б) При у=1/2
cosx=1/2
x₁=π/3 + 2πk, k∈Z
При к=2 x=π/3 + 2π*2 = π/3 + 4π = 13π/3
x₂= -π/3 + 2πk, k∈Z
При к=2 x= -π/3 + 2π*2= -π/3 + 4π = 11π/3
Ответ: 11π/3; 13π/3; 5π.
использовал в решении формулы сокращенного умножения
=================================================