Puzzle Solving - How to Transform (eqn 1) to (eqn 2)?

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In summary, the conversation discusses the equation f(x) = f(x1)*f(x-x1) / [ (cot(x1) + cot(x-x1) ] and its solution f(x) = 1 / (sin(x)). The speaker admits that it is easy to show that the solution fits the equation, but is unsure how to obtain it. They also clarify that x1 represents x_1 and that there is an additional restriction of 0 < x_1 < x.
  • #1
fled143
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I am reading an article that shows this equation

(eqn 1) f(x) = f(x1)*f(x-x1) / [ (cot(x1) + cot(x-x1) ]

an it continue that the solution to it is

(eqn 2) f(x) = 1 / (sin(x) ).

I admit that it is indeed easy to show that eqn 2 does fit to eqn 1 but I don't really have idea how to get eqn 2 out of eqn 1. Will anybody share their idea how to do this stuff? This puzzles me because it seems easy but I just don't know how to start it.
 
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  • #2
Can you check and make sure you wrote this down correctly.

Also, I assume x1 means [itex]x_1[/itex].

Also, [itex]x_1[/itex] can be anything I want?

Every detail to a question is important. There is no such thing as text talk in mathematics. ;)
 
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  • #3
Im sorry for the incomplete information.

0< x_1 < x is the additional restriction.
 

1. What is the process for transforming equations?

The process for transforming equations involves manipulating and rearranging the terms and variables in an equation to create a new equation that is equivalent to the original. This can be done by using algebraic rules and properties, such as combining like terms, distributing, and isolating variables.

2. Why would I need to transform an equation?

There are several reasons why someone might need to transform an equation. One common reason is to simplify the equation and make it easier to solve or understand. Transforming equations can also help in finding solutions to equations or in proving mathematical concepts.

3. What are some common techniques used for transforming equations?

Some common techniques used for transforming equations include factoring, completing the square, and applying the quadratic formula. Other techniques include substitution, elimination, and cross-multiplication.

4. Can any equation be transformed into another equation?

Yes, any equation can be transformed into another equation as long as the operations performed on both sides of the equation are mathematically valid and maintain the equality between the two equations. However, the resulting equation may not always be simpler or more useful than the original.

5. Is there a specific order in which equations should be transformed?

There is no specific order in which equations should be transformed. However, it is important to follow the rules of algebra and maintain the equality between the two equations throughout the transformation process. It may also be helpful to start with simpler transformations and work towards more complex ones.

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