Prove that tan^2 A -tan^2B=(sin^2A-sin^2B)/cos^2A.cos^2B)
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take l.h.s=r.h.s
sin^2A/cos^2A-sin^2A/cos^2A
(sin^2A-sin2^A)/(cos^2A.cos^2A)
sin^2A/cos^2A-sin^2A/cos^2A
(sin^2A-sin2^A)/(cos^2A.cos^2A)
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