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)

NS
Answered by Nathaniel S. Further Mathematics tutor

2964 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Give the general solution to (d2y/dx2) - 2dy/dx -3y = 2sinx


When using the method of partial fractions how do you choose what type of numerator to use and how do you know how many partial fractions there are?


explain the eigenvalue problem


A curve has the equation (5-4x)/(1+x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences