Using the Wolfram Alpha website, the site gave me three alternate forms of $z = \tan (x + ix)$, but my concern is on the third alternate form which has to do with $\sin (x)$, $\cos (x)$, $\sinh (x)$, and $\cosh (x)$. The question here is: How can I obtain that alternate form of $\tan (x + ix)$ mathematically?
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@Lisbeth & Martin R, the link you've both provided shows the alternate form of $tan (z)$ for its real and imaginary parts. What I am after is the real and imaginary part of $tan (x + ix)$; expressing them in terms of $cos (x)$, $sin (x)$, $cosh (x)$ and $sinh (x)$. – Nzewi Ernest Kenechukwu Jul 13 '19 at 06:44
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2@NzewiErnestKenechukwu: Just set $y = x$ in those expressions ... – Martin R Jul 13 '19 at 06:46
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Do you mean $$z=\tan(x+iy)$$? – Dr. Sonnhard Graubner Jul 13 '19 at 07:03
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@Dr.SonnhardGraubner, did you click the link associated with my question? The link described as 'Using the Wolfram Alpha Website' – Nzewi Ernest Kenechukwu Jul 13 '19 at 07:58