(1-сos4x)²/4+(1+cos4x)²/4=5/8
1-2cos4x+cos²4x+1+2cos4x+cos²4x=5/2
2+2cos²4x=5/2
2cos²4x=1/2
2*(1+cos8x)/2=1/2
2(1+cos8x)=1
1+cos8x=1/2
cos4x=-1/2
4x=-2π/3+2πk U 4x=2π/3+2πk
x=-π/6+πk/2 U x=π/6+πk/2
0≤-π/6+πk/2≤π U 0≤π/6+πk/2≤π
0≤-1+3k≤6 U 0≤1+3k≤6
1≤3k≤7 U -1≤3k≤5
1/3≤k≤7/3 U -1/3≤k≤5/3
k=1⇒x=-π/6+π/2=π/3
k=2⇒x=-π/6+π=5π/6
k=0⇒x=π/6
k=1⇒x=π/6+π/2=2π/3
Ответ 4 корня