Define tanh(t) in terms of exponentials

Whenever you have a define by exponentials question start with:

sinh(t)=0.5(et-e-t)      and    cosh(t)=0.5(et+e-t)

We know tanh(t)=sinh(t)/cosh(t)

               tanh(t)=0.5(et-e-t)/0.5(et+e-t)

                        =(et-e-t)/(et+e-t)  <=  0.5 cancels. This is the answer, though if you prefer, you can tidy it up by multiplying through by et

                        =(e2t-1)/(e2t+1)

Related Further Mathematics A Level answers

All answers ▸

Given that z = a + bj, find Re(z/z*) and Im(z/z*).


Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.


Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?


How do you show that the centre of a group is a subgroup


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences