Question

help solve with all steps
csch^-1 ((-1)/(2 sqrt(30)))

Answer 1

\[csch^{-1}(\frac{-1}{2 \sqrt{30}}) =x \\ \frac{-1}{2 \sqrt{30}}=csch(x) \\ \frac{-1}{2 \sqrt{30}}=\frac{2}{e^{x}-e^{-x}} \\ (e^x-e^{-x})\frac{-1}{2 \sqrt{30}}=2 \\ \text{ multiply } e^x \text{ on both sides you will wind up with a quadratic } \\ \text{ however if you know already that } \\ csch^{-1}(x)=\ln(\sqrt{1+\frac{1}{x^2}}+\frac{1}{x})\]
then just input -1/2(sqrt(30)) into that