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derivative problem

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

Reply 1

qgujxj39

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.

Reply 2

Gr8

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?