One of the addition formulae for hyperbolic functions (very similar to the addition formulae for trig functions) is . As a consequence, .
Given the vector function I need to find the tangent unit vector . The denominator is the absolute value of the vector derivative . I write an expression for :
I don't think this could be wrong since it's pretty straight forward. It requires zero intelligence, you just apply the definition directly. However, I can't seem to obtain the same expression given in the book:
I can see that , which suggests that they just multiplied the numerator and denominator of by . However I can't get the demonator in the form . I'm confused by the algebra, I can't show that .