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Solving Trig Identities

Date: 12/31/2001 at 10:33:33
From: Sarah
Subject: Trig. identities (proving)

Please can you help me prove this trig. identitity:

   Sin X Cot X = Cos X

A breakdown of exactly how to do it correctly would be much 
appreciated for future reference.


Date: 12/31/2001 at 10:46:48
From: Doctor Jaffee
Subject: Re: Trig. identities (proving)

Hi Sarah,

There are three steps that I have found to be extremely helpful in 
solving most trigonometry identities.

1. Transform each function in terms of the sine or cosine function;  
   for example, tan x = sin x/cos x, cot x = cos x/sin x, 
   sec x = 1/cos x, csc x = 1/sin x.

2. Perform "appropriate" algebra steps; for example, reduce fractions, 
   get common denominators and add or subtract fractions, transform 
   complex fractions to simple fractions, etc. This step is the most 
   difficult for most students.

3. Apply the "Fundamental Theorem of Trigonometry"; that is, 
   cos^2(x) + sin^2(x) = 1.

Now, if we apply these steps to your problem: Sin X Cot X = Cos X,
Step 1 says change cot x in terms of sin x and cos x.

You would cancel in step 2 and the problem is solved. This is a case 
where step 3 is unnecessary.

Give it a try and if you are having difficulties, or if you want to 
discuss this some more, write back. Good luck.

- Doctor Jaffee, The Math Forum   
Associated Topics:
High School Trigonometry

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