Verwijderde inhoud Toegevoegde inhoud
|
|
|
:<math>
\begin{align}
\arcsin x &{}= -i\,\logln\left(i\,x+\sqrt{1-x^2}\right) &{}= \arccsc \frac{1}{x}\\
\arccos x &{}= -i\,\logln\left(x+\sqrt{x^2-1}\right) = \frac{\pi}{2}\,+i\logln\left(i\,x+\sqrt{1-x^2}\right) = \frac{\pi}{2}-\arcsin x &{}= \arcsec \frac{1}{x}\\
\arctan x &{}= \frac{i}{2}\left(\logln\left(1-i\,x\right)-\logln\left(1+i\,x\right)\right) &{}= \arccot \frac{1}{x}\\
\arccot x &{}= \frac{i}{2}\left(\logln\left(1-\frac{i}{x}\right)-\logln\left(1+\frac{i}{x}\right)\right) &{}= \arctan \frac{1}{x}\\
\arcsec x &{}= -i\,\logln\left(\sqrt{\frac{1}{x^2}-1}+\frac{1}{x}\right) = i\,\logln\left(\sqrt{1-\frac{1}{x^2}}+\frac{i}{x}\right)+\frac{\pi}{2} = \frac{\pi}{2}-\arccsc x &{}= \arccos \frac{1}{x}\\
\arccsc x &{}= -i\,\logln\left(\sqrt{1-\frac{1}{x^2}}+\frac{i}{x}\right) &{}= \arcsin \frac{1}{x}
\end{align}</math>
|
