How do you prove that #-2cosbeta(sin alpha - cosbeta) = (sin alpha - cosbeta)^2 + cos^2beta - sin^2alpha#?

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Answer 1 · 2017-02-15T20:02:36

You're going to want to expand everything on the right.

#RHS#:

#(sin alpha - cos beta)(sin alpha - cos beta) + (cos beta + sin alpha)(cos beta - sin alpha)#

#sin^2alpha - 2cosbetasinalpha + cos^2beta + cos^2beta -sin^2alpha#

#2cos^2beta - 2cosbetasinalpha#

#2cosbeta(cos beta - sin alpha)#

#-2cosbeta(sin alpha - cos beta)#

The left hand side now equals the right hand side, so the identity has been proved.

Hopefully this helps!