tan(A+B).tan(A-B)=sin^2A-Sin^2B/cos^2A-sin^2B
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tan(A+B)-tan(A-B) =sin2B/(cos^2B-sin^2A)
L.H.S.
=sin(A+B)/cos(A+B)-sin(A-B)/cos(A-B)
=[sin(A+B).cos(A-B)-cos(A+B).sin(A-B)]/cos(A+B).cos(A-B).
=sin{(A+B)-(A-B)}/(cosA.cosB-sinA.sinB).(cosA.cosB+sinA.sinB).
=sin2B/(cos^2A.cos^2B-sin^2A.sin^2B).
=sin2B/[(1-sin^2A).cos^2B-sin^2A.(1-cos^2B)]
=sin2B/[cos^2B-sin^2A.cos^2B-sin^2A+sin^2A.cos^2B].
=sin2B/(cos^2B-sin^2A). , proved.
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