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

$:. RHS=LHS$

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