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 From: Doctor Link Subject: Re: How do you work this problem? Hi April, I'm glad you chose to write about verifying identities, because that 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/
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