19.12. Verify the following hyperbolic identities: (a) cosh?. (b) cosh(z1 + z2) = cosh z1 cosh z2 + sinh sinh z = = 1. 21 sinh 2. (c) sinh(z1 + z2) sin cosh z2 + cosh z1 sinh z2. 21 (d) cosh 2z = cosh...

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My question is about Complex function and Derivative and Integral.

The given equations must be proved.

I showed in the upload photo.

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Extracted text: 19.12. Verify the following hyperbolic identities: (a) cosh?. (b) cosh(z1 + z2) = cosh z1 cosh z2 + sinh sinh z = = 1. 21 sinh 2. (c) sinh(z1 + z2) sin cosh z2 + cosh z1 sinh z2. 21 (d) cosh 2z = cosh z + sinh? z, sinh 2z = 2 sinh z cosh z. tanh z1 + tanh z2 (e) tanh(z1 + z2) 1+ tanh z1 tanh z2