How do you verify the identity (tanx+tany)/(1-tanxtany)=(cotx+coty)/(cotxcoty-1)?

1 Answer
Apr 19, 2017

see below

Explanation:

Right Hand Side:
color(blue)((cot x+cot y)/(cot xcoty-1)=color(red)((1/tanx + 1/tany)/(1/tanx * 1/tany -1

color(red)(=((tany+tanx)/(tanxtany))/((1-tanxtany)/(tanx tany)

color(red)(=(tany+tanx)/(tanxtany) *(tanx tany)/ (1-tanxtany)

color(red)(=(tany+tanx)/cancel(tanxtany) *cancel(tanx tany)/ (1-tanxtany)

color(red)(=(tany+tanx)/ (1-tanxtany)

color(red)(=(tanx+tany)/ (1-tanxtany)

color(red)(= Left Hand Side