Expert: Paul Klarreich - 1/25/2008

Question
im really stuck on this identity,

(tanx+tany)(1-cotxcoty) + (cotx+coty)(1-tanxtany)=0

anyone help would be helpful, thanks

Answer
Questioner:   mike
Category:  Advanced Math
Private:  No
 
Subject:  Identities
Question:  im really stuck on this identity,

(tanx+tany)(1-cotxcoty) + (cotx+coty)(1-tanxtany)=0

anyone help would be helpful, thanks
Hi, Mike:

It's a lot of writing, but the world is covered with pencils, so....
 
Look at the left side:

(tanx+tany)(1-cotxcoty) + (cotx+coty)(1-tanxtany)

Multiply it all out:

tan x + tan y - tan x cot x cot y - tan y cot x cot y + cotx+coty - cot x tan x tan y - cot y tan x tan y

Use the fact that  cot A tan A = 1:

tan x + tan y - cot y - cot x  + cotx + coty -  tan y - tan x  

Now see if any terms drop out:

****** + tan y - cot y - cot x  + cotx + coty -  tan y *******  

****** ******* - cot y - cot x  + cotx + coty ******* *******  

****** ******* ******* - cot x  + cotx ****** ******* *******  

****** ******* ******* ********  ******* ****** ******* *******  

Doesn't leave much, does it?