If x=a sec theta+b tan theta ,y=a tan theta +b sec theta prove that x 2 -y \u200b2 =a 2 -b 2

If x=a sec theta+b tan theta ,y=a tan theta +b sec theta prove that x

1.	If x=a sec theta+b tan theta ,y=a tan theta +b sec theta prove that x 2 -y \u200b2 =a 2 -b 2
Answer» Given: x = a sec\xa0{tex}\\theta{/tex} + b tan\xa0{tex}\\theta{/tex}\xa0and y = a tan\xa0{tex}\\theta{/tex}\xa0+ b sec\xa0{tex}\\theta{/tex}ATQx2 - y2 = (a sec\xa0{tex}\\theta{/tex}\xa0+ b tan\xa0{tex}\\theta{/tex})2 - (a tan\xa0{tex}\\theta{/tex}\xa0+ b sec\xa0{tex}\\theta{/tex})2\xa0= a2 sec2\xa0{tex}\\theta{/tex}\xa0+ b2 tan2\xa0{tex}\\theta{/tex}\xa0+ 2ab sec\xa0{tex}\\theta{/tex}\xa0tan\xa0{tex}\\theta{/tex}\xa0- (a2 tan2\xa0{tex}\\theta{/tex}\xa0+ b2 sec2\xa0{tex}\\theta{/tex}\xa0+ 2ab tan\xa0{tex}\\theta{/tex}\xa0sec\xa0{tex}\\theta{/tex})=a2 (sec2\xa0{tex}\\theta{/tex}\xa0- tan2\xa0{tex}\\theta{/tex}) - b2 (sec2\xa0{tex}\\theta{/tex}\xa0- tan2\xa0{tex}\\theta{/tex})= a2 - b2Hence proved.