Show that cosh^2(x)-sinh^2(x)=1

In exponential form, sinh^2(x)=1/4(e^2x+e^-2x-2), cosh^2(x)=1/4(e^2x+e^-2x+2). Therefore cosh^2(x)-sinh^2(x)=1/4(2-(-2))=4/4=1, as required. 

TD
Answered by Tutor80806 D. Further Mathematics tutor

7195 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Write sin(4x) in terms of sin and cos.


Explain why the equation tanx + cotx = 1 does not have real solutions.


Find roots 'a' and 'b' of the quadratic equation 2(x^2) + 6x + 7 = 0


What is the value of x from (x+2)^2=4


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning