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- atsuoLv 61 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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