Question #e752a

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Answer 1 · 2017-01-07T15:00:38

If x is in Q1 then both $sinx and cosx$ are positive

Given $sinx=3/5=>cosx=sqrt(1-(3/5)^2)=4/5$

If y is in Q2 then $siny ->+ve and cosy_.-ve$

Given $siny=24/25=>cosy=-sqrt(1-(24/25)^2)=-7/25$

Now

$sin(x+y)=sinxcosy+cosxsiny$

$=>sin(x+y)=3/5(-7/25)+4/5xx24/25$

$=>sin(x+y)=(-21+96)/125=75/125=3/5$

Check
$x=sin^-1(3/5)~~36.87^@->"in " Q_1$

$y=sin^-1(24/25)~~106.26^@->"in " Q_2$

$sin(x+y)=sin(36.87+106.26)^@~~3/5$