Question #1fa9c

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Answer 1 · 2017-10-15T08:09:44

$7/25.$

$cosx+cosy=1/3 rArr 2cos((x+y)/2)cos((x-y)/2)=1/3.....(1).$

$sinx+siny=1/4 rArr 2sin((x+y)/2)cos((x-y)/2)=1/4.......(2).$

$:. (2) -: (1) rArr tan((x+y)/2)=3/4.$

Knowing that, $cos2theta=(1-tan^2theta)/(1+tan^2theta),$ we have,

$cos(x+y)=cos(2((x+y)/2)),$

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

$=(1-9/16)/(1+9/16).$

$rArr cos(x+y)=7/25.$

Enjoy Maths.!