Question

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!

Answer 1

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

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

So we have that

`sin(x+y)=sinx*cosy+cosx*siny=(8^2+15^2)/17^2=1`

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