Need help with a trigonometric expression

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Homework Help Overview

The discussion revolves around a trigonometric expression involving the equivalence of two forms: ##\frac 1 2 (sin(2x)+1)## and ##sin^2(x+\frac \pi 4)##. Participants are exploring the identities and transformations necessary to demonstrate this equivalence.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for relevant trigonometric identities and question the adequacy of the original poster's attempts. There is a suggestion to express both forms in terms of sine and cosine to facilitate comparison.

Discussion Status

The discussion has progressed with some participants providing guidance on how to approach the problem by expanding the expressions. The original poster has indicated a breakthrough in their understanding after applying the sine addition formula, although the specifics of their solution are not detailed.

Contextual Notes

There was an initial lack of relevant equations provided by the original poster, which led to some critique from other participants regarding the adequacy of their attempts. The conversation reflects adherence to forum guidelines on providing assistance without giving direct solutions.

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Homework Statement


Just a simple problem, I need to take the expression##\frac 1 2 (sin(2x)+1)## and show it is equivalent to ##sin^2(x+\frac \pi 4)##, and I can't seem to manage to find the way to do so, so I would appreciate some insight.

Homework Equations


N/A

The Attempt at a Solution


Effectively messing around with the trigonometric identities to no avail.
 
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You will need some relevant equations... N/A doesn't get you any further

And 'dunno' doesn't qualify as an attempt at solution.
 
I do intend to help you with this really very simple problem, but I have to adhere to the rules (see PF guidelines ).
For starters: what do you get when you write out both in terms of ##\ \sin x\ ## and ##\ \cos x \ ## ?
 
I guess I needed to write some identities there, sorry.
Following your comment I used sin (a + b) = sin a.cos b + sin b.cos a and got the wanted expression, thanks for the help.
 
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