If cosα+2cosβ+3cosγ=sinα+2sinβ+3sinγ=0 then the value of sin 3α+8sin3β+27sin3γ is
sin(α+β+γ)
3sin(α+β+γ)
18sin(α+β+γ)
sin(α+2β+γ)
Let a=cosα+isinαb=cosβ+isinβc=cosγ+isinγThen, a+2b+3c=(cosα+2cosβ+3cosγ) +i(sinα+2sinβ+3sinγ)=0⇒a3+8b3+27c3=18abc⇒cos3α+8cos3β+27cos3γ=18cos(α+β+γ)and sin3α+8sin3β+27sin3γ=18sin(α+β+γ)