If cosα + cosβ + cosγ = 0 = sinα + sinβ + sinγ(i) cos 3α + cos 3β + cos 2γ = 3 cos(α+β+γ) (ii) sin 3α + cos 3β + sin 3γ = 3 sin (α+β+γ)

Question

If cosα + cosβ + cosγ = 0 = sinα + sinβ + sinγ, then prove that 

(i) cos 3α + cos 3β + cos 2γ = 3 cos(α+β+γ) 

(ii) sin 3α + cos 3β + sin 3γ = 3 sin (α+β+γ)

Answer 1

Let a = cisα, b = cisβ, c = cisγ