Question #32f48

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Answer 1 · 2016-07-28T23:20:27

$x = {72.2}^{\circ}$ $x=72.2^@$

$y = {26.6}^{\circ}$ $y=26.6^@$

Given

$cosx+cosy=1.2.....(1)$

$sinx+siny=1.4......(2)$

Squaring and addig (1) and (2)

$cos^2x+sin^2x+cos^2y+sin^2y+2cosxcosy+2sinxsiny=1.4^2+1.2^2$

$=>2+2cos(x-y)=3.4$

$=>2cos(x-y)=1.4$

$=>x-y=cos^-1(0.7)$

$=>x-y=45.6^@......(3)$

Deviding (2) by (1)

$(sinx+siny)/(cosx+cosy)=1.4/1.2$

$=>(2sin((x+y)/2)cos((x-y)/2))/ (2cos((x+y)/2)cos((x-y)/2))=7/6$

$=>tan((x+y)/2)=7/6$

$=>(x+y)/2=tan^-1(7/6)$

$(x+y)/2=49.4^@$

$=>x+y=98.8^@$ .......(4)

Adding (3) & (4)

$=>2x=98.8^@+45.6^@=144.4^@$

$:.x=72.2^@$

Subtracting (3) from (4)

$2y=98.8^@-45.6^@=53.2^@$

$:.y=26.6^@$