Proving Identities: Cos^2(x)= (1+Cos2x)/2

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Homework Help Overview

The discussion revolves around proving the trigonometric identity cos²(x) = (1 + cos(2x)) / 2, which falls under the subject area of trigonometric identities.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss starting with the right-hand side of the equation and applying the double angle formula. There is an attempt to manipulate the expression using known identities, and one participant questions the validity of their steps.

Discussion Status

The discussion appears to be progressing with some participants offering guidance and affirming the steps taken by others. There is a sense of collaboration, but no explicit consensus has been reached regarding the proof.

Contextual Notes

Participants are working within the constraints of proving an identity, which may involve assumptions about the trigonometric functions and their properties.

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Homework Statement


prove: cos^2(x)= (1+cos2x)/(2)


Homework Equations


i broke the cos^2(x) down to 1-sin^2(x)?


The Attempt at a Solution

 
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It's easier to start with the right hand side. Just apply the double angle formula on the right.
 
this is what i did:

= (1+cos2x)/(2)
= (1+ (2cos^2(x)-1))/(2)
= 2cos^2 (x)/2
cos^2(x)=cos^2(x)

look good?
 
Yeah looks ok.
 
awsome thanksman
 

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