1)![sin(\frac{5\pi}{4}+a)=-sin(\frac{3\pi}{4}-a)\\\sin\frac{5\pi}{4}*cosa+sina*cos\frac{5\pi}{4}=-(sin\frac{3\pi}{4}*cosa-sina*cos\frac{3\pi}{4})\\sin(\pi+\frac{\pi}{4})*cosa+sina*cos(\pi+\frac{\pi}{4})=-sin(\pi-\frac{\pi}{4})*cosa+sina*cos(\pi-\frac{\pi}{4})\\-sin\frac{\pi}{4}*cosa+sina*-cos\frac{\pi}{4}=-sin\frac{\pi}{4}*cosa+sina*-cos\frac{\pi}{4}](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B5%5Cpi%7D%7B4%7D%2Ba%29%3D-sin%28%5Cfrac%7B3%5Cpi%7D%7B4%7D-a%29%5C%5C%5Csin%5Cfrac%7B5%5Cpi%7D%7B4%7D%2Acosa%2Bsina%2Acos%5Cfrac%7B5%5Cpi%7D%7B4%7D%3D-%28sin%5Cfrac%7B3%5Cpi%7D%7B4%7D%2Acosa-sina%2Acos%5Cfrac%7B3%5Cpi%7D%7B4%7D%29%5C%5Csin%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%29%2Acosa%2Bsina%2Acos%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-sin%28%5Cpi-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%2Acosa%2Bsina%2Acos%28%5Cpi-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C-sin%5Cfrac%7B%5Cpi%7D%7B4%7D%2Acosa%2Bsina%2A-cos%5Cfrac%7B%5Cpi%7D%7B4%7D%3D-sin%5Cfrac%7B%5Cpi%7D%7B4%7D%2Acosa%2Bsina%2A-cos%5Cfrac%7B%5Cpi%7D%7B4%7D)
<em><u>Доказано. </u></em>
![cos(a-\frac{2\pi}{3})=cos(a+\frac{4\pi}{3})\\cosa*cos\frac{2\pi}{3}+sina*sin\frac{2\pi}{3}=cosa*cos\frac{4\pi}{3}-sina*sin\frac{4\pi}{3}\\cosa*cos(\pi-\frac{\pi}{3})+sina*sin(\pi-\frac{\pi}{3})=cosa*cos(\pi+\frac{\pi}{3})-sina*sin(\pi+\frac{\pi}{3})\\cosa*-cos\frac{\pi}{3}+sina*sin\frac{\pi}{3}=cosa*-cos\frac{\pi}{3}-(-sin\frac{\pi}{3})*sina](https://tex.z-dn.net/?f=cos%28a-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%3Dcos%28a%2B%5Cfrac%7B4%5Cpi%7D%7B3%7D%29%5C%5Ccosa%2Acos%5Cfrac%7B2%5Cpi%7D%7B3%7D%2Bsina%2Asin%5Cfrac%7B2%5Cpi%7D%7B3%7D%3Dcosa%2Acos%5Cfrac%7B4%5Cpi%7D%7B3%7D-sina%2Asin%5Cfrac%7B4%5Cpi%7D%7B3%7D%5C%5Ccosa%2Acos%28%5Cpi-%5Cfrac%7B%5Cpi%7D%7B3%7D%29%2Bsina%2Asin%28%5Cpi-%5Cfrac%7B%5Cpi%7D%7B3%7D%29%3Dcosa%2Acos%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%29-sina%2Asin%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%29%5C%5Ccosa%2A-cos%5Cfrac%7B%5Cpi%7D%7B3%7D%2Bsina%2Asin%5Cfrac%7B%5Cpi%7D%7B3%7D%3Dcosa%2A-cos%5Cfrac%7B%5Cpi%7D%7B3%7D-%28-sin%5Cfrac%7B%5Cpi%7D%7B3%7D%29%2Asina)
<em><u>Доказано. </u></em>
1) -8+7(-x-2)=6
-8-7x-14=6
-7x=6+8+14
-7x=28
x=28/(-7)
x=-4
2) 7-2x=37-7(x+3)
7-2x=37-7x-21
-2x+7x=37-21-7
5x=9
x=9/5
x=1,8
3) -3x+1-3(x+3)=-2(1-x)+2
-3x+1-3x-9=-2+2x+2
-3x-3x-2x=-2+2-1+9
-8x=8
x=8/(-8)
x=-1
(3х-5)²+(4х-1)(4х+1)=29
9х-30х+25+4х²-1=29
-21х+25+16х²-1=29
16х²-21х-4=0
а=16,в=-21,с=-4
Д=(-21)²-4•16•(-4)=441+256=697
х=21±√697/2•16=21±√697/32