How do you find the exact value $tan(x-y)$ if $sinx=8/17,cosy=3/5$ ?

Question

17407 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T10:37:03

The answer is $=-36/77$

We use

$cos^2x+sin^2x=1$

$cos^2y+sin^2y=1$

$sin(x-y)=sinxcosy-sinycosx$

$cos(x-y)=cosxcosy+sinxsiny$

$sinx=8/17$

$cosx=sqrt(1-sin^2x)=sqrt(1-64/289)=sqrt(225/289)=15/17$

$cosy=3/5$

$siny=sqrt(1-cos^2y)=sqrt(1-9/25)=sqrt(16/25)=4/5$

$tan(x-y)=sin(x-y)/cos(x-y)$

$=(sinxcosy-sinycosx)/(cosxcosy+sinxsiny)$

$=(8/17*3/5-4/5*15/17)/(15/17*3/5+8/17*4/5)$

$=(24/85-60/85)/(45/85+32/85)$

$=-36/77$

How do you find the exact value tan(x-y)tan(x-y) if sinx=8/17,cosy=3/5sinx=8/17,cosy=3/5?