Driving me batty CSC^4x -COT^4x; simplify.

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SUMMARY

The discussion focuses on simplifying the trigonometric expression csc4x - cot4x. The user successfully factors the expression into (csc2x + cot2x)(csc2x - cot2x). A key insight is the application of the Pythagorean identity, specifically that csc2x - cot2x equals 1. This simplification is crucial for understanding the underlying principles of trigonometric identities.

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Homework Statement



The problem is to simplify the following trig equation:

csc^4x - cot^4x

Homework Equations



There really isn't any I can think of.



The Attempt at a Solution



When I attempt to simplify csc^4x - cot^4x I arrive at the result, from factoring, (csc^2x + cot^2x)(csc^2x - cot^2x). The book shows just the addition portion of my factoring. I have asked my professor and he said that I need not worry as the exam will be multiple guess?? I however am not satisfied with guessing, and would like to know if there is some fundamental rule or operation which I have overlooked. Thanks in advance and I apologize for the eq not being in a Tex format, I'm on my phone. Take care.

Joe
 
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You can use a pythagorean trig identity with one of the factors you have.
 
Well that's embarassing... Thanks buddy. I knew it had to be something simple but I have a tendency to make things way more difficult than they are. I am assuming you were referring to csc^2x - cot^2x = 1 ?

Joe
 

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