if cos alpha + cos beta + cos gamma = 0 then prove that cos 3 alpha + cos 3 beta + cos 3 gamma = 12 cos alpha cos beta cos gamma

Givencosα+cosβ+cosγ=0 _____________(1)We knowcos3x=4cos3x-3cosxThereforecos3α+cos3β+cos3γ=4cos3α-3cosα+4cos3β-3cosβ+4cos3γ-3cosγ=4cos3α+4cos3β+4cos3γ-3cosα-3cosβ-3cosγ=4cos3α+cos3β+cos3γ-3cosα+cosβ+cosγ=4cos3α+cos3β+cos3γ-0      using equation 1=4cos3α+cos3β+cos3γWe know if a+b+c=0, then a3+b3+c3=3abc=43 cosα cosβ cosγ=12cosα cosβ cosγ

  • 19
it is in TB
 
  • 3
What are you looking for?