1. -12 • 3/4 - 3 • 5/6 = -9-2,5 = -11,5. 2. 1 - 0,6 • 5 = -2 < 1 + 0,6 • 5 = 4. 3. а) 12а - 10b - 10a + 6b = 2a - 4b; б) 4(3x - 2) + 7 = 12x - 8 + 7 = 12x - 1; в) 8х - (2х + 5) + (х - 1) = 8х - 2х - 5 + х - 1 = 7х - 6. 4. -5 (0,6c - 1,2) - 1,5c - 3 = -3c + 6 - 1,5c - 3 = -4,5c + 3; 45/10 • 4/9 + 3 = 2 + 3 = 5. 5. s = vа + ua = (v + u)а; s = (5 + 4)3 = 28 км. где s - расстояние между . 6. 7х - (5х - (3х + у)) = 7х - 5х + (3х + у) = 2х + 3х + у = 5х + у. можно подробное решение
sin2x - (1-sin²x) =0 ;
2sinxcosx -cos²x =0 ;
cosx(2sinx -cosx) =0 ;
[cosx =0 ;2sinx-cosx =0.⇔ [cosx =0 ;sinx=(1/2)cosx.⇔[cosx =0 ;tqx=1/2.
[ x=π/2 +πn ; x =arctq1/2+πn , n∈Z.
2) ;
ctq2x*cos²x - ctq2x*sin²x =0 ;
ctq2x*(cos²x - sin²x) =0 ;
ctq2x*cos2x =0 ;
sin2x =0 * * *cos2x = ± 1 ≠0→ ОДЗ * * *
2x =πn , n∈Z ;
x =(π/2)*n , n∈Z .
3) ;
3sin²x/2 -2sinx/2 =0 ;
3sinx/2 (sinx/2 -2/3) =0 ;
[sinx/2 =0 ; sinx/2 =2/3 .⇒[x/2 =πn ; x/2= arcsin(2/3) +πn ,n∈Z.⇔
[x =2πn ; x= 2arcsin(2/3) +2πn ,n∈Z.
4) ;
* *cos2α =cos²α -sin²α =cos²α -(1-sin²α)=2cos²α -1⇒1+cos2α=2cos²α * *
cos3x = 1+cos2*(3x) ; * * * α = 3x * * *
cos3x = 2cos²3x ;
2cos²3x -cos3x =0 ;
2cos3x(cos3x -1/2) =0 ;
[cos3x =0 ; cos3x =1/2 ⇒[3x=π/2+πn ; 3x= ±π/3+2πn ,n∈Z.⇔
[x=π/6+πn/3 ; x= ±π/9+(2π/3)*n ,n∈Z.