1)2сos²x-1=1-2sin²x
2sin²x+sinx-1=0
sinx=a
2a²+a-1=0
D=1+8=9
a1=(-1-3)/4=-1⇒sinx=-1⇒x=-π/4+2πn
a2=(-1+3)/4=1/2⇒sinx=1/2⇒x=(-1)^n*π/6+πn
2)cosx(cosx-√3sinx)=0
cosx=0⇒x=π/2+πn
cosx-√3sinx=0
2(1/2*cosx-√3/2*sinx)=0
2sin(π/6-x)=0
sin(π/6-x)=0⇒cos(x+π/3)=0
x+π/3=π/2+πn=x=π/6+πn
3)cos2(2x+1)-4√2sin(2x+1)=4
1-2sin²(2x+1)-4√2sin(2x+1)-4=0
2sin²(2x+1)+4√2sin(2x+1)+3=0
sin(2x+1)=a
2a²+4√2a+3=0
D=32-24=8
a1=(-4√2-2√2)/4=-1,5√2⇒sin(2x+1)=-1,5√2<-1 нет решения<br>a2=(-4√2+2√2)/4=-√2/2⇒sin(2x+1)=-√2/2⇒
2x+1=(-1)^n+1*π/4+πn
2x=-1+(-1)^n+1*π/4+πn
x=-1/2+(-1)^n+1*π/8+πn/2