prove that cos 2alphacos2beta+sin^2(alpha-beta) -sin^2(alpha+beta) =cos2(alpha+beta)
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Consider the unit vector
(u,v,w).
The cosines of the angles it forms with the axis are given by the dot products
cosα=(1,0,0)⋅(u,v,w)=u,cosβ=(0,1,0)⋅(u,v,w)=v,cosγ=(0,0,1)⋅(u,v,w)=w,
and as it is unit
u2+v2+w2=1.
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