Question 969954
Prove that (cot y - cot x) / (cot x + cot y) = sin (x-y) / (sin x + y)
start with left side
{{{(cot y - cot x) / (cot x + cot y)}}}
..
{{{((cosy/siny) - (cosx/sinx)) / ((cosx/sinx) + (cosy/siny))}}}
note: denominators (sinxsiny) cancel out
..
{{{((cosysinx) - (sinycosx)) / ((cosxsiny) + (sinxcosy))}}}
note: terms rearranged
{{{((sinxcosy) - (cosxsiny)) / ((sinxcosy) + (cosxsiny))=sin(x-y)/sin(x+y)}}}
verified: left side=right side