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if a sec θ + b tan θ + c0and p sec θ+q tan θ + r-0. Show that(pc ar(aq - bp) |
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Answer» Asecθ+Btanθ+C=0or, C=-(Asecθ+Btanθ)Psecθ+Qtanθ+R=0or, R=-(Psecθ+Qtanθ)∴, (BR-QC)²-(PC-AR)²=[B{-(Psecθ+Qtanθ)}-Q{-(Asecθ+Btanθ)}]²-[P{-(Asecθ+Btanθ)}-A{-(Psecθ+Qtanθ)}]²=(-BPsecθ-BQtanθ+AQsecθ+BQtanθ)²-(-APsecθ-BPtanθ+APsecθ+AQtanθ)²=(AQ-BP)²sec²θ-(AQ-BP)²tan²θ=(AQ-BP)²(sec²θ-tan²θ)=(AQ-BP)² (Proved) [∵, sec²θ-tan²θ=1] |
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