Question #32f48

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Answer 1 · 2016-07-28T23:20:27

#x=72.2^@#

#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^@#