How to simplify tan^-1 (a) - tan^-1 (b)??? (1 Viewer)

blackops23 · Sep 7, 2011

How do I simplify $tan^{-1}(a)\, -\, \tan^{-1}(b)?$

In my question there is an expression:

And v is for velocity, u, and k are constants.

And I need to get v in terms of t. And probably the best idea would be to simplify

Thanks for the help guys.

Amogh · Sep 7, 2011

Also, to simplify calculations you can define the two inverse tans with arbitrary variables. (a and b)

thoth1 · Sep 7, 2011

but u wanted v in terms of t so here:
$t = \tan^{-1}\frac{v}{\sqrt{k}}-\tan^{-1}\frac{u}{\sqrt{k}}$
$t+\tan^{-1}\frac{u}{\sqrt{k}} = \tan^{-1}\frac{v}{\sqrt{k}}$
$\tan (t+\tan^{-1}\frac{u}{\sqrt{k}}) = \frac{v}{\sqrt{k}}$
$\sqrt{k}\tan (t+\tan^{-1}\frac{u}{\sqrt{k}}) = v$

cutemouse · Sep 10, 2011

blackops23 said:
How do I simplify $tan^{-1}(a)\, -\, \tan^{-1}(b)?$

= arctan(a-b)/(1+ab)

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How to simplify tan^-1 (a) - tan^-1 (b)??? (1 Viewer)

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