What is the solution? If sin x=8/17, sin y= 15/17, and 0<x< π/2, 0<y<π/2; then x+y= π/2. Prove it!

1 Answer

If sinx=8/17sinx=817 then cosx=sqrt(1-8^2/17^2)=>cosx=15/17cosx=182172cosx=1517

and siny=15/17siny=1517 then cosy=sqrt(1-15^2/17^2)=>cosy=8/17cosy=1152172cosy=817

So we have that

sin(x+y)=sinx*cosy+cosx*siny=(8^2+15^2)/17^2=1sin(x+y)=sinxcosy+cosxsiny=82+152172=1

Hence because sin(x+y)=1=>x+y=pi/2sin(x+y)=1x+y=π2