Why does this expression simplify to 1-sin(x)?

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Homework Help Overview

The discussion revolves around the simplification of a mathematical expression involving trigonometric functions, specifically focusing on the expression (1-sin(x))(sin(x))-(cos(x))(0-cos(x)). Participants are trying to understand why it simplifies to 1-sin(x) as stated in the original post.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the correctness of the simplification and whether there was a typographical error in the original expression. Some are attempting to clarify the expression's components and their implications.

Discussion Status

The discussion is active, with participants exploring different interpretations of the expression. Some have provided alternative perspectives on the simplification process, while others have pointed out potential errors in the original formulation. There is no explicit consensus on the simplification yet.

Contextual Notes

There are indications of confusion regarding the original expression and its components, particularly with respect to the presence of a minus sign and the interpretation of trigonometric identities. Participants are also referencing specific values of x to test the simplification.

Jbright1406
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ok, i have this and know what it should simplify to, but why?

(1-sin(x))(sin(x))-(cos(x))(0-cos(x))


i know it simplifies to

1-sin(x)

but my book doesn't explain what exactly happens. could someone please shed some light and explain what exactly happens
 
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I think you mistyped something. It doesn't simplify to that. Try for example x =pi/4.
 
Defennder said:
I think you mistyped something. It doesn't simplify to that. Try for example x =pi/4.

I'm parsing his message as:

(1-sinx)(sin2x+cos2x)

Does that make sense?

Edit: No, I misread!
 
thats what i kept seeing.

i see it simplifies to one.

the answer in the book shows the answer i previously gave over (1-sinx)^2

then the final answer being

1 over (1-sinx)
 
[(1-sinx)(-sinx)-cosx(0-cosx)]/(1-sinx)^2

then
(1-sinx)/(1-sinx)^2

then the final being
(1)/(1-sinx)


PS sorry for the double posting
 
Jbright1406 said:
[(1-sinx)(-sinx)-cosx(0-cosx)]/(1-sinx)^2
That minus sign, which was absent in your original post, makes the whole world of difference. To simplify, just expand the numerator out and apply a trigo identity.
 

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