The fundamental period of the function fx=csin2x+sin2x+π3+cosxcosx+π3 is (where c is constant)

sin2x+sin2x+π3+cosxcosx+π3                  =sin2x+sinx2+3cosx22+cosxcosx2-3sinx2                  =sin2x+sin2x4+3cos2x4+cos2x2                  =5sin2x4+5cos2x4                  =54Hence, fx=c54 = Constant, which is periodic but has no fixed period.