Trig solve for all angles x problem

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The discussion focuses on solving the equation Sin(x) + Sin(2x) + Sin(x) * Cos(2x) + Sin(2x) * Cos(x) = 0 for all angles x. Participants suggest using trigonometric identities, specifically the double angle formulas for Sin(2x) and Cos(2x), to simplify the equation. One user mentions factoring out Sin(x) as a potential strategy but expresses uncertainty about the approach. After applying the identities, the equation is simplified, leading to a clearer path to the solution. Overall, the conversation emphasizes the importance of trigonometric identities in solving complex trigonometric equations.
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Homework Statement


Sin(x)+sin(2x)+sin(x)*Cos(2x)+sin(2x)*cos(x)=0
Solve for all angles x.

Homework Equations


Sin(2x)= 2sin(x)*cos(x)

The Attempt at a Solution


Not really sure what to do. I noticed that i could maybe factor out Sin(x), but i do not really know if that is right.

I seem to be always stuck on these kind of problems. Any general tips would greatly help me as well. Thank you
 
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So you just used double angles to get rid of sin(2x) and cos(2x)?
 
Yes I used double angles for them and I had to use the cos^2 identity also. I wish I could just scan my paper and upload it but no scanner.
 
Cool, i think i got it now. Thanks for your time.
 

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