How do you verify the identity #cosA-sinA=(cos2A)/(cosA+sinA)#?

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Answer 1 · 2016-11-12T14:12:27

See proof below

RHS
#cos(A+B)=cosAcosB-sinAsinB#

Let #B=A#

Then

#cos2A=cos^2A-sin^2A=(cosA+sinA)(cosA-sinA)#

#(cos2A)/(cosA+sinA)=(cancel(cosA+sinA)(cosA-sinA))/cancel(cosA+sinA#

#=cosA-sinA#

#=# LHS

#:. RHS=LHS#