How do you prove that csch^-1(x) = sinh^-1(1/x)?
1 Answer
Jun 13, 2018
We seek to prove that:
# csch^(-1)(x) -= sinh^(-1)(1/x) #
Let:
# u = csch^(-1)(x) => cschu=x #
# v = sinh^(-1)(1/x) => sinhv=1/x #
Then we have:
# sinhv = 1/x = 1/(cschu) = sinhu #
And as
# sinhv = sinhu iff v = u #
# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ iff sinh^(-1)(1/x) = csch^(-1)(x) \ \ \ # QED