prove that (secA secB + tanA tanB)2 - (secA tanB +tanA secB)2 = 1

L.H.S.=secAsecB+tanAtanB2-secAtanB+tanAsecB2            =sec2Asec2B+tan2Atan2B+2secAsecBtanAtanB-sec2Atan2B+tan2Asec2B+2secAsecBtanAtanB            =sec2Asec2B+tan2Atan2B+2secAsecBtanAtanB-sec2Atan2B-tan2Asec2B-2secAsecBtanAtanB            =sec2Asec2B+tan2Atan2B-sec2Atan2B-tan2Asec2B            =sec2Asec2B-sec2Atan2B+tan2Atan2B-tan2Asec2B            =sec2Asec2B-tan2B-tan2Asec2B-tan2B            =sec2B-tan2Bsec2A-tan2A            =1×1            =1            =R.H.S.Hence Proved.

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