if x = asec + btan and y = atono + bsec Prove that x2 -y2 = a2-b2

1.	if x = asec + btan and y = atono + bsec Prove that x2 -y2 = a2-b2
Answer» We\xa0have,x = asec{tex}\\theta{/tex}\xa0+ btan{tex}\\theta{/tex}\xa0and y = atan{tex}\\theta{/tex}\xa0+ bsec{tex}\\theta{/tex}LHS = (x2\xa0- y2) = (asec{tex}\\theta{/tex}\xa0+ btan{tex}\\theta{/tex})2\xa0- (atan{tex}\\theta{/tex}\xa0+ bsec{tex}\\theta{/tex})2= (a2sec2{tex}\\theta{/tex}\xa0+ b2tan2{tex}\\theta{/tex}\xa0+ 2absec{tex}\\theta{/tex}tan{tex}\\theta{/tex}) -\xa0(a2tan2{tex}\\theta{/tex}\xa0+ b2sec2{tex}\\theta{/tex}\xa0+ 2absec{tex}\\theta{/tex}tan{tex}\\theta{/tex})= a2(sec2{tex}\\theta{/tex}\xa0- tan2{tex}\\theta{/tex}) - b2(sec2{tex}\\theta{/tex}\xa0- tan2{tex}\\theta{/tex})= a2\xa0- b2\xa0= RHSTherefore, LHS = RHS

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