2(cos3x-cosx)+sin2x=0
-4sinxsin2x+sin2x=0
sin2x(-4sinx+1)=0
sin2x=0πn⇒x=πn/2,n∈z
3π/2≤πn/2≤3π
3≤n≤6
n=3⇒x=3π/2
n=4⇒x=2π
n=5⇒x=5π/2
n=6⇒x=3π
-4sinx+1=0
sinx=1/4⇒x=arcsin1/4+2πk,k∈z
x=arcsin1/4
x=π-arcsin1/4
x=2π+arcsin1/4
x=3π-arcsin1/4
Cos^2(α)=1-sin^2(α)=1-1/16=15/16
5cos^2(α)-1=5*15/16-1=75/16-1=59/16