Ответы
Ответ дал:
0
116)
![cos2x-2cosx=0 cos2x-2cosx=0](https://tex.z-dn.net/?f=cos2x-2cosx%3D0)
![2cos^2x-1-2cosx=0 2cos^2x-1-2cosx=0](https://tex.z-dn.net/?f=2cos%5E2x-1-2cosx%3D0)
![2cos^2x-2cosx-1=0 2cos^2x-2cosx-1=0](https://tex.z-dn.net/?f=2cos%5E2x-2cosx-1%3D0)
Замена:
![|a| leq 1 |a| leq 1](https://tex.z-dn.net/?f=%7Ca%7C+leq+1)
![2a^2-2a-1=0 2a^2-2a-1=0](https://tex.z-dn.net/?f=2a%5E2-2a-1%3D0)
![D=(-2)^2-4*2*(-1)=12 D=(-2)^2-4*2*(-1)=12](https://tex.z-dn.net/?f=D%3D%28-2%29%5E2-4%2A2%2A%28-1%29%3D12)
∅
![a_2= frac{2-2 sqrt{3} }{4} =frac{1- sqrt{3} }{2} a_2= frac{2-2 sqrt{3} }{4} =frac{1- sqrt{3} }{2}](https://tex.z-dn.net/?f=a_2%3D+frac%7B2-2+sqrt%7B3%7D+%7D%7B4%7D+%3Dfrac%7B1-+sqrt%7B3%7D+%7D%7B2%7D+)
![cosx=frac{1- sqrt{3} }{2} cosx=frac{1- sqrt{3} }{2}](https://tex.z-dn.net/?f=cosx%3Dfrac%7B1-+sqrt%7B3%7D+%7D%7B2%7D+)
∈ ![Z Z](https://tex.z-dn.net/?f=Z)
∈ ![Z Z](https://tex.z-dn.net/?f=Z)
117)
![2cos^2x+5cos( frac{ pi }{2} -x)-4=0 2cos^2x+5cos( frac{ pi }{2} -x)-4=0](https://tex.z-dn.net/?f=2cos%5E2x%2B5cos%28+frac%7B+pi+%7D%7B2%7D+-x%29-4%3D0)
![2cos^2x+5sinx-4=0 2cos^2x+5sinx-4=0](https://tex.z-dn.net/?f=2cos%5E2x%2B5sinx-4%3D0)
![2(1-sin^2x)+5sinx-4=0 2(1-sin^2x)+5sinx-4=0](https://tex.z-dn.net/?f=2%281-sin%5E2x%29%2B5sinx-4%3D0)
![2-2sin^2x+5sinx-4=0 2-2sin^2x+5sinx-4=0](https://tex.z-dn.net/?f=2-2sin%5E2x%2B5sinx-4%3D0)
![-2sin^2x+5sinx-2=0 -2sin^2x+5sinx-2=0](https://tex.z-dn.net/?f=-2sin%5E2x%2B5sinx-2%3D0)
![2sin^2x-5sinx+2=0 2sin^2x-5sinx+2=0](https://tex.z-dn.net/?f=2sin%5E2x-5sinx%2B2%3D0)
Замена:
![|a| leq 1 |a| leq 1](https://tex.z-dn.net/?f=%7Ca%7C+leq+1)
![2a^2-5a+2=0 2a^2-5a+2=0](https://tex.z-dn.net/?f=2a%5E2-5a%2B2%3D0)
![D=(-5)^2-4*2*2=9 D=(-5)^2-4*2*2=9](https://tex.z-dn.net/?f=D%3D%28-5%29%5E2-4%2A2%2A2%3D9)
∅
![a_2= frac{5-3}{4}= frac{1}{2} a_2= frac{5-3}{4}= frac{1}{2}](https://tex.z-dn.net/?f=a_2%3D+frac%7B5-3%7D%7B4%7D%3D+frac%7B1%7D%7B2%7D+)
![sinx=frac{1}{2} sinx=frac{1}{2}](https://tex.z-dn.net/?f=sinx%3Dfrac%7B1%7D%7B2%7D+)
∈ ![Z Z](https://tex.z-dn.net/?f=Z)
∈ ![Z Z](https://tex.z-dn.net/?f=Z)
118)
![sin^2x+cos( frac{ pi }{2} -x)*sin( frac{ pi }{2} -x)-2cos^2x=0 sin^2x+cos( frac{ pi }{2} -x)*sin( frac{ pi }{2} -x)-2cos^2x=0](https://tex.z-dn.net/?f=sin%5E2x%2Bcos%28+frac%7B+pi+%7D%7B2%7D+-x%29%2Asin%28+frac%7B+pi+%7D%7B2%7D+-x%29-2cos%5E2x%3D0)
![sin^2x+sinx*cosx-2cos^2x=0 sin^2x+sinx*cosx-2cos^2x=0](https://tex.z-dn.net/?f=sin%5E2x%2Bsinx%2Acosx-2cos%5E2x%3D0)
разделим почленно на cos²x≠0
![tg^2x+tgx-2=0 tg^2x+tgx-2=0](https://tex.z-dn.net/?f=tg%5E2x%2Btgx-2%3D0)
Замена:![tgx=a tgx=a](https://tex.z-dn.net/?f=tgx%3Da)
![a^2+a-2=0 a^2+a-2=0](https://tex.z-dn.net/?f=a%5E2%2Ba-2%3D0)
![D=1-4*1*(-2)=9 D=1-4*1*(-2)=9](https://tex.z-dn.net/?f=D%3D1-4%2A1%2A%28-2%29%3D9)
![a_1= frac{-1+3}{2}=1 a_1= frac{-1+3}{2}=1](https://tex.z-dn.net/?f=a_1%3D+frac%7B-1%2B3%7D%7B2%7D%3D1+)
![a_2= frac{-1-3}{2}=-2 a_2= frac{-1-3}{2}=-2](https://tex.z-dn.net/?f=a_2%3D+frac%7B-1-3%7D%7B2%7D%3D-2+)
или ![tgx=-2 tgx=-2](https://tex.z-dn.net/?f=tgx%3D-2)
∈
или
∈ ![Z Z](https://tex.z-dn.net/?f=Z)
Замена:
117)
Замена:
118)
разделим почленно на cos²x≠0
Замена:
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