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Eliminte ?, 1) if x=3 sec ? + 4 tan ? and y=4 sec ?- 3 tan ?. 2) the angles of dipression of the top and bottom of 8 meter tall building from the top of multistoried building are 30° and 45° respectively.find the height of multistoried building and the distance between two buildings (?3=1.73)

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(1).:x=3sec 	heta+4	an 	heta;and;y=4sec 	heta-3	an 	heta\* Now,;multiply;x;and;y\* Rightarrow xy=12-7sec 	heta 	an 	heta\* ecause sec^2 	heta -	an^2 	heta=1\*Now,;square;x;and;y;then; add;x;and;y\* Rightarrow x^2+y^2=25(sec^2 	heta+	an^2 	heta)\* Rightarrow x^2+y^2=25(2	an^2 	heta +1)Rightarrow 	an	heta= sqrt fracx^2+y^2-2550\* Now;put;;valye 	an 	heta in;product;of ;x ; &;y\* xy=12-7(	an	heta)(sqrt	an^2	heta +1)\* xy=12-frac750(sqrt(x^2+y^2)-(50)^2)\* (2).;Look;figure;Given;that;CD=8;m,;AB=h;m;and;BC=x;m\* In;	riangle ABC\* 	an 45^circ =frachxRightarrow h=x\* In;	riangle AED\* 	an 30^circ=frach-8xRightarrow frac1sqrt3 =frach-8h\* ecause h=x\* Rightarrow h=frac8 sqrt3sqrt3 -1;m \* x=h=frac8 sqrt3sqrt3 -1;m\*Hence,;the;height;of;multistoried; building;and;the;distance;between;two;buildings;are;same;equal;to;frac8 sqrt3sqrt3 -1m

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Deependra Verma

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