Question #fc331

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Answer 1 · 2016-12-20T13:30:19

Given

$sinx+siny=1/4$

$=>2sin((x+y)/2)cos((x-y)/2)=1/4......(1)$

Also given

$cosx+cosy=1/3$

$=>2cos((x+y)/2)cos((x-y)/2)=1/3..........(2)$

Dividing (1) by (2) we get

$tan((x+y)/2)=3/4$

Now

$cot(x+y)=1/(tan(x+y))$

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

$=(1-(3/4)^2)/(2xx3/4)$

$=((16-9)/16)/(3/2)$

$=7/16*2/3=7/24$