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(c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = 1 +2 sinh?(x).

(c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = 1 +2 sinh?(x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = 1 + 2 sinh?(x). %3D
Transcribed Image Text:(c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = 1 + 2 sinh?(x). %3D
る Here defined the hyberbolie functim direetly in telm of The enponential functim ;). simh(x) This is defined by The formulu, sinhim) = ee ニ 2 ii) 11) coshu). This is de fineod by the formula; Cers h (u) = e tek 2 li1) tanhn), This is defined by The formula, -ze tanh(n) = sinh(n) ニ Crs h (n) Iv) formale, coseeh (n), This is defined by the Coseeh(n) : 2 ニ sinhen) ex eX 2 2 . cesceh(x) eX e-X v) seehin) = ニ coshin) eute 二 exten 2. '. seeh(x) = e"ten Coshin) Simhin) etek vi) coth(n) = etex %3D eneu' : coth(n) = ete- %3D Xキo ,
Transcribed Image Text:る Here defined the hyberbolie functim direetly in telm of The enponential functim ;). simh(x) This is defined by The formulu, sinhim) = ee ニ 2 ii) 11) coshu). This is de fineod by the formula; Cers h (u) = e tek 2 li1) tanhn), This is defined by The formula, -ze tanh(n) = sinh(n) ニ Crs h (n) Iv) formale, coseeh (n), This is defined by the Coseeh(n) : 2 ニ sinhen) ex eX 2 2 . cesceh(x) eX e-X v) seehin) = ニ coshin) eute 二 exten 2. '. seeh(x) = e"ten Coshin) Simhin) etek vi) coth(n) = etex %3D eneu' : coth(n) = ete- %3D Xキo ,
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