Proving sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

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Homework Help Overview

The problem involves proving the equality of two expressions involving trigonometric functions: the left-hand side (LHS) is sin² + 2cos - 1/2 + cos - cos², and the right-hand side (RHS) is 1/(1 + sec). The subject area is trigonometry, specifically focusing on identities and simplifications.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to manipulate the LHS using trigonometric identities but expresses uncertainty about their approach. Some participants question the clarity of the function arguments and suggest the need for proper notation to avoid ambiguities. Others note potential missing brackets that could affect the interpretation of the expressions.

Discussion Status

The discussion is ongoing, with participants clarifying the notation and addressing ambiguities in the expressions. There is a focus on ensuring that all terms are clearly defined to facilitate further assistance.

Contextual Notes

Participants highlight the importance of specifying function arguments and using brackets to clarify the structure of the expressions. There is an acknowledgment of the need for clearer communication to progress in the problem-solving process.

ihatemath
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ok ... here's my problem
i need to prove that the LHS = RHS


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

i tried to use the pythagarean identies and substitute the 1 and 2
but tht isn't getting me anywhere .. please help
 
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If you don't list the arguments of the functions we can't help you, also show the steps you've taken so far.
 
ummm ok .. here's what i got


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

LHS :

= sin^2 + cos + cos - sin^2 - cos^2 / 1 + sin^2 + cos^2 + cos - cos^2
... here i canceled the "sin^2" and " - sin^2" on the top and in the bottom i canceled the "cos^2" and " - cos^2"

= cos + cos - (cos)(cos) / 1 + sin^2 + cos

= cos + cos - cos^2 / sin^2 + cos^2 + sin^2 + cos

= cos + cos / sin^2 + sin^2 + cos

... I don't noe what to do from here ... am i even tackling this problem the right way ??

RHS :

1 / 1 + sec

= 1 / 1 + 1/cos
= 1 + cos ... no problems here .. jus the LHS
 
You forgot the arguments. Sin does not exist, sin(x) does etc.
 
there all sin(x) or cos(x) :-p
 
Okay then we're arriving at the next problem. I have a feeling that some brackets are missing, for example what is 1/1+sec(x) is it [tex]1+\sec(x)[/tex] or [tex]\frac{1}{1+\sec x}[/tex]. Same goes for the right hand side. Use brackets to make divisions clear.
 
itz

[tex]\frac{1}{1+\sec x}[/tex]
 
Yes, but what about the other side, similar ambiguities exist there. For me to assist you on this problem you will need to take all those ambiguities away.
 
ihatemath said:
ok ... here's my problem
i need to prove that the LHS = RHS


sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

i tried to use the pythagarean identies and substitute the 1 and 2
but tht isn't getting me anywhere .. please help

Are you trying to prove that
[tex]sin^2(x) + 2cos(x) - \frac{1}{2} + cos(x) - cos^2(x) = \frac{1}{1 + sec(x)}?[/tex]

That's actually the most reasonable way to interpret what you have written. (You've already told us what you meant on the right-hand side.
 

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