(d) cosh 2z = cosh z + sinh z, sinh 2z = 2 sinh z cosh z. tanh z1 + tanh z2 %3D 1+ tanh z1 tanh z2 (e) tanh(z1 + 2) =

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hi

My question is about Complex numbers.

I showed the question in the upload photo.

I want you to prove (d,e) parts

Thank you very much !

19.12. Verify the following hyperbolic identities:
(h) cosh(z1 t
nhl~
(d) cosh 2z =
cosh z + sinh² z,
sinh 2z = 2 sinh z cosh z.
tanh z1 + tanh z2
(e) tanh(z1 + z2)
1+ tanh z1 tanh z2
Transcribed Image Text:19.12. Verify the following hyperbolic identities: (h) cosh(z1 t nhl~ (d) cosh 2z = cosh z + sinh² z, sinh 2z = 2 sinh z cosh z. tanh z1 + tanh z2 (e) tanh(z1 + z2) 1+ tanh z1 tanh z2
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