Question 748244
what is the exact value if 0 < x < pi/2 and 0 < y < pi/2, of the cos (x+y) if the tan x = 5/3 and the sin y= 1/3
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tanx=5/3
{{{sec(x)=sqrt(tan^2(x)+1)=sqrt((25/9)+1)=sqrt((25/9)+1)=sqrt(34/9)=sqrt(34)/3)}}}
cos(x)=1/sec(x)=3/&#8730;34)
sin(x)=5/&#8730;34)
..
sin(y)=1/3
{{{cos(y)=sqrt(1-sin^2(y))=sqrt(1-1/9)=sqrt(8)/3}}}
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cos(x+y)=cos(x)cos(y)-sin(x)sin(y)=[3/&#8730;34*&#8730;8/3]-[5/&#8730;34*/3)]