Prove that (cosA+sinA)/(cosA-sinA)-(cosA-sinA)/(cosA+sinA)=2tan2A

Steps to prove (cosA+sinA)/(cosA-sinA)-(cosA-sinA)/(cosA+sinA)=2tan2A

Take L.H.S

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

[Take L.C.M]

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

=(cos^2A+sin^2A+2cosA.sinA-cos^2A-sin^2A+2cosA.sinA)/(cos^2A-sin^2A)

=4sinA.cosA/cos2A

=2(2sinA.cosA)/cos2A

[2sinA.cosA=sin2A]

=2(sin2A/cos2A)

=2tan2A

=R.H.S

Hence (cosA+sinA)/(cosA-sinA)-(cosA-sinA)/(cosA+sinA)=2tan2A is proved.

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