Using Trig Identities to Simplify

Date: 7/26/96 at 22:5:58
From: Anonymous
Subject: Using Trig. Identities to Simplify

I have tried to solve this problem using many identities, but it 
doesn't get me anywhere.  The problem is

((sin @ - 1)/cos @) - (cos @/(sin @ -1))

I have been trying to get the equation all in sines, but I haven't
had much luck.  I tried getting a common denominator of 
cos @ sin @ -cos @ and used a lot of identities, and I ended up with 
what I started  with.  The problem says to subtract and simplify.  I 
know what the answer is, 2 tan @, but I can't get it.  HELP!

Date: 7/27/96 at 11:33:41
From: Doctor Anthony
Subject: Re: Using Trig. Identities to Simplify


Putting the two expressions on a common denominator we have:

      (sin x - 1)^2 - cos^2 x
    = ------------------------
         cos x(sin x - 1)


       sin^2 x - 2sin x + 1 - cos^2 x
    =  -------------------------------
         cos x(sin x - 1)


        2sin^2 x - 2sin x
    =   -----------------
         cos x(sin x - 1)


        2sin x(sin x - 1)
    =   -----------------
         cos x(sin x - 1)


    =  2tan x
   
        
-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/