Question

prove that cos 2alphacos2beta+sin^2(alpha-beta) -sin^2(alpha+beta) =cos2(alpha+beta)

Answer 1

Answer:

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.