1
2sinx=-√2
sinx=-√2/2
x=(-1)^(n+1)*π/4+πn,n∈z
2
cos(x/2+π/4)=-1
x/2+π/4=π+2πn
x/2=3π/4+2πn
x=3π/2+4πn,n∈z
3
1-cos²x-2cosx+2=0
cosx=a
a²+2a-3=0
a1+a2=-2 U a1*a2=-3
a1=-3⇒cosx=-3<-1 нет решения<br>a2=1⇒cosx=1⇒x=2⇒n,n∈z
4
Разделим на cos²x
2tg²x+tgx-1=0
tgx=a
2a²+a-1=0
D=1+8=9
a1=(-1-3)/4=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=(-1+3)/4=0,5⇒tgx=0,5⇒x=arctg0,5+πn,n∈z
5
2sin²x-4sinxcosx+5cos²x-2sin²x-2cos²x=0
3cos²x-4sinxcosx=0
cosx*(3cosx-4sinx)=0
cosx=0⇒x=π/2+πn,n∈z
3cosx-4sinx=0/cosx
3-4tgx=0
tgx=3/4
x=arctg0,75+πn,n∈z
6
sin3x-cos3x=0/cos3x
tg3x-1=0
tg3x=1
3x=π/4+πn
x=π/12+πn/3,n∈z
x={π/12;5π/12;3π/4;13π/12}