Associated Topics || Dr. Math Home || Search Dr. Math

### Verify the Identity

```Date: 04/17/2003 at 20:30:56
From: April
Subject: How do you work this problem?

Verify the identity:      csc x
------------- = cos x
tan x + cot x
```

```
Date: 04/18/2003 at 16:46:15
Subject: Re: How do you work this problem?

Hi April,

happens to be something that I really enjoy.

The first thing that you should do when trying to verify an identity
is have a list of all the most common identities beside you. You can
refer to the following FAQ to view such a list:

Trigonometry Formulas - Dr. Math FAQ
http://mathforum.org/dr.math/faq/formulas/faq.trig.html

Equipped with this knowledge you can now begin to try to verify this
identity. What I find to be a very useful method is to rewrite the
more complicated side (the side with more terms in it - in this case
the left side) in terms of sine and cosine. This can be especially
effective when the simpler side is mostly in terms of sine and
cosine, as in this case.

Another effective method is to look for parts of the problem where,
using identities, you can cancel things out. For example, suppose you
are trying to verify the identity:

2       2
(csc x)*(sin x) = sin x + cos x

Since we know that csc x is the reciprocal of sin x, we can rewrite
the left side as:

1
----- * (sin x)
sin x

which is, of course, just 1. To finish this problem you can rewrite
the right side as 1 because of the Pythagorean identity:

2       2
sin x + cos x = 1

Now let's go back to your problem. To rewrite the csc x part in terms
of sine or cosine you simply make use of the fact that:

1
-----
sin x

is its reciprocal.

Now how could you change the tan x and the cot x to only sines and
cosines? Try to use the general techniques I mentioned above.

If you are still having trouble feel free to write back and I will
assist you further. Thanks again for writing in!

- Doctor Link, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search