I need to rewrite two expressions in terms of exponentials and simplify.
First expression: 2cosh(ln x) –> Answer should be x + 1/x
Second expression: ln(cosh x + sinh x) + ln(cosh x – sinh x) –> Do not know answer
A step by step would be helpful, I really need to learn this and am sinking at the moment. Thank you in advance.
Best Answer
This might help, (by definition):
$$\cosh x = \frac{e^x + e^{-x}}{2}$$
Replace x with $\ln x$ and simplify, note that $e^{\ln x} = x$
Use a similar idea for your second expression and note that:
$$ \sinh x = \frac{e^x - e^{-x}}{2}$$