Question

Плиз)срочно надо)Разложите на множители.1)sin3α+sinα2)cos2α+cos3α3)cosx-cos3x4)siny-sin5y

Answer 1

1)3(sina+sina) 3)3(cosx-cosx) 4)5(siny-siny)

Answer 2

1)sin3α+sinα=2sin(3α+α)/2*cos(3α-α)=2sin2α*cosα       sinα+sinβ=2sin(α+β)/2*cos(α-β)/2
2)cos2α+cos3α=2cos(2α+3α)/2*cos(2α-3α)=2cos5α/2*cosα/2    cosα+cosβ=2cos(α+β)/2*cos(α-β)/2
3)cosx-cos3x=-2sin(x+3x)/2*sin(x-3x)/2=-2sin2x*sin(-x)=2sin2xsinx 
cosα-cosβ=-2sin(α+β)/2*sin(α-β)/2
4)siny-sin5y=2sin(y-5y)/2*cos(y+5y)=2sin(-2y)*cos3y=-2sin2y*cos3y
sinα-sinβ=2sin(α-β)/2*cos(α+β)/2