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cos2x= cos^2x-sin^2x =1-2sin^2x
sin2x=2sinx cosx
sin3x= sinx( 1-2sin^2x) +2sinxcos^2x
=sinx-2sin^3x +2sinx -2sin^3x
sin3x= 3sinx -4sin^3x
sinx+sin3x = 4sinx-4sin^3x = 4sinx ( 1-sin^2x) =4sinx cos^2x
4sinxcos^2x = cos x
cosx (4sinxcos x-1) =0
cos x=0
x= pi/2 +kpi k=0,1,2... ( El angulo es cuadrangular ,por eso el periodo es kpi y no 2kpi)
O bien
4sinx cosx =1
O sea
2 sin2x =1
sin2x= 1/2
2x= pi/6+2kpi
x= pi/12+ kpi