Question

Question #e752a

Answer 1

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`