Решите уравнения! 2sin^2 x/2-3 sin x/2+1=0 3tg^2+2tgx-1=0

1) sin(x/2)=t⇒2t^2-3t+1=0⇒t1=(3+√9-8)/4=(3+1)/4=1; t2=(3-√9-8)/4=(3-1)/4=1/2 sin(x/2)=1⇒x/2=π/2+2πn⇒x=π+4πn sin(x/2)=1/2⇒x/2=(-1)^n*π/6+πn⇒x=(-1)^n*π/3+2πn 2) 3tg^2+2tgx-1=0tgx=t⇒3t^2+2t-1=0⇒t1=(-1+√1+3)/3=1/3; t2=(-1-√1+3)/3=-1tgx=1/3⇒x=arctg(1/3)+πntgx=-1⇒x=-π/4+πn

1) cos^2(x)-cos(2x)=sin(x)

cos^2((x)-sin^2(x))=sin(x)

sin^2(x)-sin(x)=0

sin(x)(sin(x)-1)=0

a) sin(x)=0

x=pi*n

 

б) sin(x)-1=0

sin(x)=1

x=(pi/2)+2*pi*n

 

2) cos(2x)+sin^2(x)=cos(x)

( cos^2(x)-sin^2(x))+sin^2(x)=cos(x)

cos^2(x)-cos(x)=0

cos(x)(cos(x)-1)=0

a) cos(x)=0

x=(pi/2)+pi*n

б) cos(x)-1=0

cos(x)=1

x=2*pi*n

(2)/(5)*(5.5m-2)-0.8m < 4.6m-(3)/(4)*(3.6m-1.6)

0,4*(5.5m-2)-0.8m < 4.6m-0,75*(3.6m-1.6)

2,2m-0.8-0.8m< 4.6m-2.7m+1.2

1.4m-0.8< 1.9m+1.2

-0.8-1.2< 1.9m-1.4m

-2< 0.5m

m> -4

 

m ∈ (-4; + бесконеч)