Came up with a second personalized proof (is it correct)

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In summary, the conversation discusses the proof of sin(90 + theta) = cos(theta). One person points out that angle COD is not necessarily theta, and the other person explains that the only construction that can be assumed is that angles ODE and ODA are right angles. The first person also mentions using the fact that the two angles in a right triangle are complementary to prove that COD is theta. The conversation then shifts to discussing whether AOE is an isosceles triangle and the point is clarified that segment OD does not have to be perpendicular to segment AE.
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  • #2
proof of sin(90 + theta) = cos(theta)
 

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  • #3
Well, I wouldn't say "by construction angle COD is also theta". Since OD is perpendicular to AE, the only thing that is true "by construction" is that angle ODE and ODA are right angles. Now, you can they show that COD is theta by using the fact that the two angles in a right triangle are complementary- but you should show that.
 
  • #4
Wait. Am I missing something here. Shouldn't COD be 45-(theta/2) ?

AOE is an isosceles triangle. The perpendicular is also the angle bisector, right? Or have I understoond something wrong here?
 
  • #5
Sorry.. after I looked at it... segment OD is not perp to segment AE.. and it doesn't have to be. I came up with a diff steps which I edited in the picture that I attached..
 

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1. How do you come up with a personalized proof?

Coming up with a personalized proof involves thoroughly understanding the problem and finding a unique approach that is tailored to your specific strengths and knowledge. It requires creativity, critical thinking, and a deep understanding of the subject matter.

2. What makes a personalized proof different from a standard proof?

A personalized proof is different from a standard proof because it is specifically tailored to your individual thought process and style of problem-solving. It may not follow the traditional steps or methods used in a standard proof, but it still effectively demonstrates the validity of the argument.

3. How do you know if your personalized proof is correct?

You can determine if your personalized proof is correct by carefully examining each step and ensuring that it logically follows from the previous one. It should also be supported by evidence and be able to withstand scrutiny from other scientists and mathematicians in the field.

4. What should you do if you are unsure about the correctness of your personalized proof?

If you are unsure about the correctness of your personalized proof, it is always a good idea to seek feedback from other experts in the field. They may be able to offer valuable insights and suggestions to help improve your proof or identify any potential errors.

5. Can a personalized proof be used in a professional setting?

Yes, a personalized proof can be used in a professional setting as long as it effectively demonstrates the validity of the argument and is supported by evidence. In fact, personalized proofs can often lead to new and innovative solutions in the scientific community.

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