how to prove that tan iz=-i tanh z ?

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Question : Prove that tan iz=-i tanh z ?

Answer :

A complex number z is written as

\[z=x+iy\]

where x and y are real numbers.

By the formula

\[tan (iz) = \frac{sin (iz)}{cos (iz)}\]

Now sin (iz) =i sinh z and cos (iz) = cosh z

\[tan (iz) = \frac{i sinh z}{cosh z} = i tanh z\]

\[tanh z = \frac{1}{i} tan (iz)\]

Thus we proved that tan iz=-i tanh z ?


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