# Thread: Hyperbolic Function (Simultaneous Equation)

1. ## Hyperbolic Function (Simultaneous Equation)

Q: If $x$ and $y$ satisfy the equations

$\mathrm{cosh}x \mathrm{cosh}y = 2$
$\mathrm{sinh}x \mathrm{sinh}y = -1$

Show that $x = -y = \pm \ln (1 + \sqrt{2})$
__________________
My Problem: I did this question by changing the hyperbolic function in terms of $e$ but did not get the correct answer. Can someone do this question and show me how they obtained the correct answer? Thanks in advance.

2. Originally Posted by Air
Q: If $x$ and $y$ satisfy the equations

$\mathrm{cosh}x \mathrm{cosh}y = 2$
$\mathrm{sinh}x \mathrm{sinh}y = -1$

Show that $x = -y = \pm \ln (1 + \sqrt{2})$
__________________
My Problem: I did this question by changing the hyperbolic function in terms of $e$ but did not get the correct answer. Can someone do this question and show me how they obtained the correct answer? Thanks in advance.

$\cosh(x+y)=\cosh x \cosh y+\sinh x \sinh y$ ?

And then transforming it into exponentials

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### how to solve hyperbolic simultaneous equation

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