Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    derive the identity

    (sech^2 x)/(1+tanh^2 x) = sech2x


    and


    sech x = (2e^x)/(e^2x +1)





    help me out.i cant solve these.it is under principle of integral evaluation.thanks
    Offline

    12
    ReputationRep:
    Perhaps this isn't what you're looking for, but the first one can be done using the fact that  \mathrm{sech}\ x = \dfrac{1}{\mathrm{cosh} \ x} , and  \mathrm{tanh} \ x = \dfrac{\mathrm{sinh} \ x}{\mathrm{\cosh} \ x}, and by using Osborn's rule on a certain double-angle identity for cosine.

    The second can be done from the definition  \mathrm{cosh} \ x = \dfrac{e^x + e^{-x}}{2}
    Offline

    15
    I don't see why you're talking about derivatives and integrals, as you don't need to use either.

    We have, by definition:

    \sinh x = \dfrac{e^x - e^{-x}}{2}

    \cosh x = \dfrac{e^x + e^{-x}}{2}

    \tanh x = \dfrac{\sinh x}{\cosh x}

    \mathrm{sech} x = \dfrac{1}{\cosh x}

    Use these to prove the identities.
    Offline

    0
    ReputationRep:
    (Original post by tommm)
    I don't see why you're talking about derivatives and integrals, as you don't need to use either.

    We have, by definition:

    \sinh x = \dfrac{e^x - e^{-x}}{2}

    \cosh x = \dfrac{e^x + e^{-x}}{2}

    \tanh x = \dfrac{\sinh x}{\cosh x}

    \mathrm{sech} x = \dfrac{1}{\cosh x}

    Use these to prove the identities.
    I have heard your decent at maths, just wondering have you studied any AEA maths? How hard did you find it compared to A-level (if you have studied it).
    Also would you say it is harder than Step I or even Step II? How similar would it be to them?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 12, 2009

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.