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e179285
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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...
I don't know how to start...
sin(nx) = sin((n-1)x+x)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...
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.
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.
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.
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.
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.