Derive an identity that transforms sin(α+β+γ) into a sum of products of sines and/or cosines of the individual numbers α, β, γ.

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  1. sin(α+β+γ) , I will use sin(a+b+c) for easier typing
    = sin( (a+b) +c)
    = sin(a+b)cos c + cos(a+b)sin c
    = (sinacosb + cosasinb)(cosc) + (cosacosb - sinasinb)sinc
    = sinacosbcosc + cosacoscsinb + cosacosbsinc - sinasinbsinc

    now put back your α,β, and γ

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