1. ## Inverse trigonometric function

arc tan [1/{(x^2)-1}^(1/2)].....mod x >1.
I am asked to write it in the simplest form.....how do i proceed?

2. Originally Posted by tariq_h_tauheed
arc tan [1/{(x^2)-1}^(1/2)].....mod x >1.
I am asked to write it in the simplest form.....how do i proceed?
How does your book define "simplest form" for similar exercises? Are you maybe supposed to "rationalize the denominator" for "simplest form"...?

3. The answer in the book is itself an inverse trigonometric function....actually the answer is in the order of arc sec......but i don't know the way to proceed.

4. Hello, tariq_h_tauheed!

Write in simplest form: . $\arctan\left(\frac{1}{\sqrt{x^2-1}}\right)$

Let: . $\theta \;=\;\arctan\left(\frac{1}{\sqrt{x^2-1}}\right) \quad\hdots\quad\text{then: }\:\tan\theta \:=\:\frac{1}{\sqrt{x^2-1}} \:=\:\frac{opp}{adj}$

$\theta$ is in a right triangle with: $opp = 1,\;adj = \sqrt{x^2-1}$

Code:
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*  |
x    *     |
*        | 1
*           |
* θ            |
* - - - - - - - - *
√(x²-1)
Using Pythagorus, we get: . $hyp = x$

Then: . $\csc\theta \:=\:\frac{x}{1} \:=\:x$

Therefore: . $\theta \;=\;\text{arccsc}\,x$ . .
(simplest form )
.