Question

Preciso de ajuda, por favor!!! Simplifique a expressão: Y= sen(x+PI/3) - cos(x+PI/3)

Answer 1

$sen(x+\pi/3) - cos(x+\pi/3)\\\\ sen(x+y)=senx*cosy+seny*cosx\\ cos(x+y)=cosx*cosy-senx*seny\\\\ sen(x+\pi/3)=senx*cos(\pi/3)+sen(\pi/3)*cosx\\ sen(x+\pi/3)=(1/2)senx+(\sqrt{3}/2)cosx\\\\ cos(x+\pi/3)=cosx*cos(\pi/3)-senx*sen(\pi/3)\\cos(x+\pi/3)= (1/2)cosx-(\sqrt{3}/2)senx\\\\\\ sen(x+\pi/3)-cos(x+\pi/3)=\\\\ ((1/2)senx+(\sqrt{3}/2)cosx)-((1/2)cosx-(\sqrt{3}/2)senx)\\\\1/2senx+\sqrt{3}/2sen+\sqrt{3}/2cosx-1/2cosx\\\\ senx( \frac{\sqrt{3}+1}{2}) +cosx(\frac{\sqrt{3}-1}{2})$