Why are equations written in double angle form?

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SUMMARY

Equations are often converted into double angle form to simplify calculations and reduce the potential for errors. The double angle formulas, such as sin(2θ) = 2sin(θ)cos(θ), provide a more compact representation that is easier to memorize and utilize in problem-solving. This transformation is particularly beneficial when dealing with unknown quantities, as it streamlines the process and minimizes complexity.

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  • Study the derivation and applications of double angle formulas in trigonometry
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Homework Statement


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I guess this is a general question. in the book, it was originally in a normal form, but it was then converted into a double angle form, which I would have to use double angle formula to compute, so what's the point of simplifying in the first place?

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The Attempt at a Solution

 
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I guess it depends on what your unknown quantities are. The formulae in the gray box are much simpler, so there is less opportunity to make a mistake. That would be one advantage. Also, if it is something that you are memorizing, it is less to memorize, rather than all of those sin(theta)cos(theta) etc, for example.
 
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scottdave said:
I guess it depends on what your unknown quantities are. The formulae in the gray box are much simpler, so there is less opportunity to make a mistake. That would be one advantage. Also, if it is something that you are memorizing, it is less to memorize, rather than all of those sin(theta)cos(theta) etc, for example.
I guess you are right, its more compact, easier to remember.
 

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