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### Strategies for Proving Trigonometric Identities

```Date: 05/19/2003 at 18:01:42
From: Will
Subject: Proving Trigonometric Identities

In class this week, we learned about proving trig identities and we
had a fair bit of homework relating to it. I was able to get most of
them, but this question really stumped me. Prove the identity:

1 - sin x             1
--------- = tan x + -----
1 + sin x           cos x

```

```
Date: 05/19/2003 at 18:23:49
From: Doctor Schwa
Subject: Re: Proving Trigonometric Identities

Hi Will,

I have some basic tricks that I use when trying to prove trig
identities.  They are:

1) Rewrite everything in terms of sin and cos. (In your
problem, this means converting tan x to sin x/cos x.)

2) Start by working on whichever side looks more complicated.

3) If you have fractions, always think about making common
denominators.

4) When you have something with 1+sin or the like, think
about multiplying top and bottom by the conjugate (1-sin).

5) Look for familiar identities like sin^2 + cos^2 = 1 that
you can use.

In this particular case, I think that if you start by multiplying the
left side by (1-sin)/(1-sin), then something nice should happen.
Or you may want to make a common denominator first.

Give those hints a try, and see where they leads, then write back if
you feel stuck again.

Enjoy,

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

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