Question

If the value of $\tan hx=\frac{1}{2}$, show that $x=\frac{1}{2}\ln 3$

Answer 1

$\Rightarrow \frac{e^x-e^{-x}}{e^x+e^{-x}}=1/2$

$\Rightarrow e^x=3e^{-x}$

$\Rightarrow e^{2x}=3$

$\Rightarrow 2x=ln3$

$\Rightarrow x=\frac{1}{2}ln3$