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### 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/
```
Associated Topics:
High School Trigonometry

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