Quandaries and Queries


My name is Monica and I am a student in college.
I was very curious about how to prove that arcsech x = ln[(1 + (1-x2)(1/2)) /  x ]
I know that sechy = x
which equals 1/coshy
= 2/(ey + e-y). But i am absolutely clueless after that!
I really would like to know ASAP, so if you can help, I would appreciate it!
Thanks alot.


Hi Monica,

You are correct that is sech y = x then

x = 2/(ey + e-y)

Multiply both sides by (ey + e-y) to get

x (ey + e-y) = 2

Now multiply both sides by ey and the equation becomes

x (ey)2 + x = 2 ey, or

x (ey)2 - 2 ey + x = 0

This is a quadratic in ey which you can solve using the general quadratic formula.



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