Author Topic: Inverse Trig - Writing in Algebraic Expressions - Need help (Read 1492 times) Tweet Share

squance · « **on:** August 30, 2008, 10:22:54 pm »

I can't seem to get the right answer to this question...

Write cosh (2arctanh x) as an algebraic expression in x.
i let y = 2 arctanh x
x/2 = tanh x

And I used the 1 - tanh^2 y = sech^2 y identity...

But I can't seem to get the answer of (1+ x^2)/(1-x^2)

I got 1/sqrt (1-4x^2)

HELP!!!

Mao · « **Reply #1 on:** August 31, 2008, 09:34:42 pm »

$\begin{align*} \mbox{cosh }(2\mbox{arctanh }x) &=2\mbox{cosh}^2\; (\mbox{arctanh }x)-1\\ &= 2\cdot \left(\frac{1}{\sqrt{1-x^2}}\right)^2-1\; \cdots \;[1]\\ &= \frac{2}{1-x^2}-\frac{1-x^2}{1-x^2}\\ &= \frac{1+x^2}{1-x^2}\\ \end{align*}$

[1] was derived as follows:
$\begin{align*} \mbox{Let }y &=\mbox{arctanh }x\\ \mbox{tanh }y &= x\\ \mbox{tanh}^2\; y &= x^2\\ 1-\mbox{sech}^2\; y &=x^2\\ \mbox{cosh}^2\; y &= \frac{1}{1-x^2}\\ \mbox{cosh (arctanh }x) &= \frac{1}{\sqrt{1-x^2}}\\ \end{align*}$

squance · « **Reply #2 on:** August 31, 2008, 10:13:22 pm »

Hey thanks

But I actually solved this question with some help from some people on IRC

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Author Topic: Inverse Trig - Writing in Algebraic Expressions - Need help (Read 1492 times) Tweet Share

squance

Inverse Trig - Writing in Algebraic Expressions - Need help

Mao

Re: Inverse Trig - Writing in Algebraic Expressions - Need help

squance

Re: Inverse Trig - Writing in Algebraic Expressions - Need help

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