1
(1-cos2x)²/4+(1+cos2x)²/4=5/8
2-4cos2x+2cos²2x+2+4cos2x+2cos²2x-5=0
4cos²2x-1=0
(2cos2x-1)(2cos2x+1)=0
cos2x=1/2⇒2x=+-π/3+2πn⇒x=+-π/6+πn,n∈z
cos2x=-1/2⇒2x=+-2π/3+2πk⇒x=+-π/3+πk,k∈z
2
(cos3x-cos7x)+(sin2x-sin6x)=0
2sin5x*sin2x-2sin2x*cos4x=0
2sin2x*(sin5x-cos4x)=0
sin2x=0⇒2x=πn⇒x=πn/2,n∈z
sin5x-sin(π/2-4x)=0
2sin(9x/2-π/4)*cos(x/2+π/4)=0
sin(9x/2-π/4)=0⇒9x/2-π/4=πk⇒9x/2=π/4+πk⇒x=π/18+2πk/9,k∈z
cos(x/2+π/4=0⇒x/2+π/4=π/2+πt⇒x/2=π/4+πt⇒x=π/2+2πt,t∈z
3
1/2cos(x/2-3x/2)+1/2cos(x/2+3x/2)-1/2cos(x-3x)+1/2cos(x+3x)-1/2cos(2x-3x)+1/2cos(2x+3x)=0
1/2cosx+1/2cos2x-1/2cos2x+1/2cos4x-1/2cosx+1/2cos5x=0
1/2(cos4x+cos5x)=0
1/2*2cos(9x/2)*cos(x/2)=0
cos(9x/2)=0⇒9x/2=π/2+πn⇒x=π/9+2πn/9,n∈z
cos(x/2)=π/2+πk⇒x=π+2πk,k∈z
4
5sin²x-4sinxcosx-cos²x-4sin²x-4cos²x=0/cos²x
tg²x-4tgx-5=0
tgx=a
a²-4a-5=0
a1+a2=4 U a1*a2=-5
a1=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=5⇒tgx=5⇒x=arctg5+πk,k∈z