sen(2x)=2senxcosx
cos(2x)=cos^2x-sen^2x
sen(3x)=2sexcosx*cosx+(cos^2x-sen^2x)senx=
=2sexcos^2x+cos^2xsenx-sen^3x
cos(3x)=(cos^2x-sen^2x)*cosx-2senxcosx*sex=
=2sexcos^2x+cos^2xsenx-sen^3x
2sexcos^2x+cos^2xsenx-sen^3x+
+2sexcos^2x+cos^2xsenx-sen^3x=1
4sencos^2x+2cos^2xsex-2sen^3x=1
4[senx(1-sen^2x)+2(1-sen^2x)-2sen^3x]=1
4sex-4sen^2x+2-2sen^2x-2sen^3x=1
-2sen^3x-6sen^2x+4sen^x=1
senx(-2sen^2x-6senx+4)=1
senx=1 cioè x=TT/2+2kTT prima soluzione
-2sen^2x-6senx+4-1=0
2sen^2x+6senx-3=0
senx=[-6+radq(60)]/4
x=arcosen[(-6+2rad15)/4]+2kTT seconda soluzione
senx=-6-radq(60)
x=arcosen[(-6-2rad15)/4]+2kTT terza soluzione