Show that cos(tan^(-1) v) = 1/(sqrt{1 + v^2})

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- November 12th 2008, 08:13 AM #1

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- November 12th 2008, 08:18 AM #2

- November 12th 2008, 08:44 AM #3

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I prefer the way Chris did this but since he got in first (and I just

**have**to put in my oar!) here's another way:

Use trig identities. [tex]tan^2(\theta)+1= sec^2(\theta)= 1/cos^2(\theta)[/itex] so

Replacing by , that gives [tex]cos(tan^{-1}(v))= \frac{1}{\sqrt{1+ tan^2(tan^{1}(v))}= \frac{1}{\sqrt{1+ v^2}}.

- November 12th 2008, 05:43 PM #4

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- November 12th 2008, 07:34 PM #5