How to prove this?

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  • atsuo
    Lv 6
    1 month ago

    The determinant

    = sinαcosβcosγ + cosαcosβsinγ + 0*(-sinβ)sinβ

     - (sinαsinβsinγ + cosα(-sinβ)cosγ + 0*cosβcosβ)

    = sinαcosβcosγ + cosαcosβsinγ - sinαsinβsinγ + cosαsinβcosγ

    RHS

    = sin((α+β)+γ)

    = sin(α+β)cosγ + cos(α+β)sinγ

    = (sinαcosβ + cosαsinβ)cosγ + (cosαcosβ - sinαsinβ)sinγ

    = sinαcosβcosγ + cosαsinβcosγ + cosαcosβsinγ - sinαsinβsinγ

    So the determinant = RHS

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