Q. 455.0( 2 Votes )

If A secθ + B tan

Answer :

Formula: - (i) sec2θ – tan2θ = 1


Given: -


(i) Asecθ + Btanθ + C = 0


C = – (Asecθ + Btanθ)


(ii) Psecθ + Qtanθ + R = 0


R = – (Psecθ + Qtanθ)


taking L.H.S


(BR – QC)2 – (PC – AR)2 = ((B – (Psecθ + Qtanθ)) – (Q – (Asecθ + Btanθ)))2 – P( – (Asecθ + Btanθ)) – A( – (Psecθ + Qtanθ)))2


(BR – QC)2 – (PC – AR)2 = ( – BPsecθ – BQtanθ + AQsecθ + BQtanθ)2 – ( – APsecθ – BPtanθ + APsecθ + AQtanθ)2


(BR – QC)2 – (PC – AR)2 = (AQ – BP)2sec2θ – (AQ – BP)2tan2θ


(BR – QC)2 – (PC – AR)2 = (AQ – BP)2(sec2θ – tan2θ)


using formula(i)


(BR – QC)2 – (PC – AR)2 = (AQ – BP)2


L.H.S = R.H.S


Hence, Proved.


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