Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((ex-e-x)/2)/((ex+e-x)/2) 1 - tanh2(x) = 1-((ex-e-x)/(ex+e-x))2  = ((e2x+e-2x+2)-(e2x+e-2x-2))/(ex+e-x)2 = (2ex.2e-x)/(ex+e-x)2 = 4/(ex+e-x)2 = sech2x

CB
Answered by Chris B. Further Mathematics tutor

5112 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Solve x^3=1 giving all the roots between -pi<=theta<=pi in exponential form


Split x^4/[(x^2+4)*(x-2)^2] into partial fractions and hence differentiate it


Prove by induction the sum of n consecutive positive integers is of the form n(n+1)/2.


The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (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