prove (sinx+siny)/(cosx-cosy) = -cot(x-y/2)

Question

(sinx+siny)/(cosx-cosy) = -cot(x-y/2)

use left as given

Answer 1

(sinx+siny)/(cosx-cosy)=-cot([x-y]/2)

 

2sin([x+y]/2)(cos[x-y]/2)

_____________________     =

 

-2sin([x+y]/2)(sin([x-y]/2)

 

cancel 2sin([x+y]/2) top and bottom

 

-cos([x-y]/2)

___________ =

 

sin([x-y]/2)

 

-cot([x-y]/2)   because cotθ=cosθ/sinθ