Solve cosxcos(-x) - sinxsin(-x) = 1

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Homework Help Overview

The discussion revolves around the trigonometric identity involving the equation cosxcos(-x) - sinxsin(-x) = 1, exploring the properties of cosine and sine functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of trigonometric identities, particularly the even and odd properties of sine and cosine functions. There are attempts to simplify the expression and questions about the resulting forms.

Discussion Status

Several participants have provided insights into the simplification process, with some noting the connection to angle addition formulas. There appears to be a productive exchange of ideas, although no consensus has been reached on a final approach.

Contextual Notes

Participants express uncertainty about their simplifications and the implications of the signs in the trigonometric identities being used. There is an acknowledgment of the complexity of the problem despite its apparent simplicity.

ravey_dotson
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cosxcos(-x) - sinxsin(-x) = 1

I know I'm making it harder than it is, but I can't seem to figure it out.
Any help would be appreciated.

RaveN
 
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cos(-x)=cos(x). sin(-x)=-sin(x).
 
When I plugged those in then I get cosx2 - sinx2 = 1 and then I get completely lost.
 
When I plug them in I get cos(x)^2+sin(x)^2=1. There are two minus signs associated with the sin(x)^2.
 
Because it's -sin to begin with. I knew I was making it too hard. Thanks.
 
Another way: isn't the l.h.s. in the form of an angle addition formula?
 
Not with the correct signs! It's cos2(x)+ sin2(x)!
 
It is cos(x+(-x)). That is another way to do it.
 

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