Prove that cosA-sinA/cosA+sinA=sec2A-tan2A

Steps to prove cosA-sinA/cosA+sinA=sec2A-tan2A

Take R.H.S sec2A-tan2A

=sec2A-tan2A

=1/cos2A-sin2a/cos2A

=1-sin2A/cos2A

=sin^2A+cos^2A-2sinAcosA/cos^A-sin^A

=(cosA-sinA)^2/(cosA-sinA)(cosA+sinA)

=cosA-sinA/cosA+sinA

=L.H.S

Hence cosA-sinA/cosA+sinA=sec2A-tan2A is proved

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