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Asked Sep 20, 2019
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Problem 1 in attached image

151/04-06, F2019, WORKSHOP 2
Problem 1 - The hyperbolic sine and cosine functions are defined as follows
e + e-
2
e - e-
sinh x
cosh
2
Using the above definition in terms of exponential functions show the formulas
a) cosh2 z- sinh2
1
C =
IC
CO
= cosh 2x
b) cosh2 I+sinh
tonts
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151/04-06, F2019, WORKSHOP 2 Problem 1 - The hyperbolic sine and cosine functions are defined as follows e + e- 2 e - e- sinh x cosh 2 Using the above definition in terms of exponential functions show the formulas a) cosh2 z- sinh2 1 C = IC CO = cosh 2x b) cosh2 I+sinh tonts

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Expert Answer

Step 1

Given,

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e-e -x sinhx 2 e e cosh x = 2

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Step 2

Part (a): To show

...
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cosh2 x-sinh2x =1 LHS cosh2 x-sinh2 x (cosh x-sinhx)(coshx +sinh x) X -x e -e e e e -e e +e 2 2 2 2 ex e-e e e e e e 2 2 2e 2e* 2 2 = e.e* -x+x = e = e° =1 = RHS

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