- #1

- 27

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sqrt(1-β

^{2}) = sqrt(2*(1-β)).

How do you show this mathematically? I have no idea. Thanks! :)

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- Thread starter mps
- Start date

- #1

- 27

- 0

sqrt(1-β

How do you show this mathematically? I have no idea. Thanks! :)

- #2

- 10,122

- 1,280

sqrt(1-β^{2}) = sqrt(2*(1-β)).

How do you show this mathematically? I have no idea. Thanks! :)

Let [itex]\epsilon = 1 - \beta[/itex] , then substitute [itex]\beta = 1 - \epsilon[/itex]. You get

sqrt([itex]1 - (1 -2 \beta \epsilon + \epsilon^2)[/itex]) = sqrt([itex]1 - (1 - 2 (1 - \epsilon) \epsilon + \epsilon^2)[/itex]

Take the limit as [itex]\epsilon[/itex] goes to zero. You might need a bit of calculus to do that. bit basically you keep all the terms proportioanl to [itex]\epsilon[/itex] and trhow out all high order temrs proportional to [itex]\epsilon^2[/itex].

Last edited:

- #3

- 27

- 0

sqrt([itex]1 - (1 -2 \beta \epsilon + \epsilon^2)[/itex])

I think you might have an extraneous β here, but thanks a lot!!! I get it now :)

- #4

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- #5

- 27

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Thank you! :)

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