Proving Reduction Formula

In summary, a reduction formula is a mathematical tool used to simplify complicated expressions. Proving reduction formula is important because it helps solve complex problems and understand mathematical concepts. The steps involved in proving reduction formula vary but typically involve identifying patterns, making substitutions, and using mathematical techniques. Scientists use reduction formula in fields such as physics, chemistry, and engineering. However, there may be limitations to its applicability and it is important to consider them when using it in scientific research.
  • #1
e179285
24
0
If I n =integral sin (nx) dx/sinx,prove that In =2sin((n-1)x)/n-1 +In-2 for all integers n>(egual) .


I don't know how to start...
 
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  • #2
Since you are given the formula, the obvious approach is to use induction.
 
  • #3
e179285 said:
If I n =integral sin (nx) dx/sinx,prove that In =2sin((n-1)x)/n-1 +In-2 for all integers n>(equal) .

I don't know how to start...
sin(nx) = sin((n-1)x+x)
=sin((n-1)x)∙cos(x) + cos((n-1)x)∙sin(x)​

is a good place to start.
 

What is a reduction formula?

A reduction formula is a mathematical tool used to simplify a complicated expression into a more manageable form. It involves repeatedly applying the same mathematical operation to the original expression, reducing it to a simpler form each time.

Why is proving reduction formula important?

Proving reduction formula is important because it allows us to solve complex mathematical problems by breaking them down into smaller, more manageable steps. It also helps us to better understand the underlying principles and relationships between different mathematical concepts.

What are the steps involved in proving reduction formula?

The steps involved in proving reduction formula may vary depending on the specific formula being used, but typically involve identifying a pattern or relationship between the terms in the original expression, making a substitution or change of variables, and using mathematical techniques such as induction, integration, or differentiation to simplify the expression.

How do scientists use reduction formula?

Scientists use reduction formula in a variety of fields, including physics, chemistry, and engineering. It is particularly useful in solving problems involving complex physical systems and in deriving equations that describe the behavior of these systems.

Are there any limitations to reduction formula?

While reduction formula is a powerful tool, it may not be applicable to all mathematical problems. Some expressions may not have a simple reduction form, and in some cases, the reduction process may not be feasible or may lead to incorrect results. It is important to carefully consider the limitations and assumptions of reduction formula when using it in scientific research.

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