Find an expression for :

csc^2 (tan^-1 (3/x))

in terms of x

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- Oct 24th 2009, 11:32 AMsamtheman17expression
Find an expression for :

csc^2 (tan^-1 (3/x))

in terms of x - Oct 24th 2009, 12:34 PMadkinsjr
I think this is what the problem looks like?

$\displaystyle csc^2(Arctan(\frac{3}{x}))$

Arctan is just one way of writing the inverse tangent function.

to solve this, let $\displaystyle \theta=Arctan(\frac{3}{x})$.

Therefore, $\displaystyle tan(\theta)=\frac{3}{x}$

and

$\displaystyle csc^2(Arctan(\frac{3}{x}))=csc^2(\theta)=1+cot^2(\ theta)=1+\frac{1}{tan^2(\theta)}$

So now you can write this in terms of

$\displaystyle tan(\theta)=\frac{3}{x}$

$\displaystyle csc^2(Arctan(\frac{3}{x}))=1+\frac{1}{\frac{9}{x^2 }}=1+\frac{x^2}{9}$ - Oct 24th 2009, 12:42 PMadkinsjr
Note, I edited my original post because I messed up on the final line. So if you already looked at it, look again. It's fixed now. That should be the expression you're looking for.

- BTW, this kind of question probably should have been posted in the trignometry section, since these are inverse trig functions. - Oct 24th 2009, 01:20 PMsamtheman17
thank you! makes so much sense now :)