Solving Identity Question: (cosx)^2 = (1 + cos2x)/2

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Homework Help Overview

The discussion revolves around the identity involving the cosine function, specifically the equality (cosx)^2 = (1 + cos2x)/2. Participants are exploring the derivation and recognition of this identity within the context of integration.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster inquires about the derivation of the identity and whether it is a known result. Some participants affirm its validity and reference its derivation from the double angle formula for cosine.

Discussion Status

The conversation includes affirmations of the identity's recognition among participants, with some providing insights into its derivation. However, there is no explicit consensus on the depth of explanation or the steps involved in reaching the identity.

Contextual Notes

The original poster references a worked example involving integration, suggesting a potential application of the identity in that context. There may be assumptions about prior knowledge of trigonometric identities among participants.

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Homework Statement



In a worked example I have of an integration it states the integral of (cosx)^2 = the integral of (1 + cos2x)/2

How is this equality reached?

Is this a known identity, (cosx)^2 = (1 + cos2x)/2 ?

Thank you.


Homework Equations





The Attempt at a Solution

 
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Yes.
 
Yep, that's a very well-known identity, derived from very simple algebra from ##\cos\left(2\cdot x\right)=2\cdot\cos^2\left(x\right)-1##
 
cos(x + x) = … ? :wink:
 

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