Question

Find and imaginary tan​

Answer 1

Answer:

I think that the simpler way is to write:

sinz=sin(x+iy)=sinxcos(iy)+cosxsin(iy)=sinxcoshy+icosxsinhy

cosz=cos(x+iy)=cosxcos(iy)+sinxsin(iy)=cosxcoshy−isinxsinhy

tanz=sinxcoshy+icosxsinhycosxcoshy−isinxsinhy⋅cosxcoshy+isinxsinhycosxcoshy+isinxsinhy=

=sinxcosx+isinhycoshycosh2y−sin2x=sin2x+isinh2y2cosh2y−2sin2x+1−1=sin2x+isinh2ycos2x+cosh2y

Your way seems also good but a bit more complicated.

Edit note: x was written y by mistake in two of expressions which I corrected so that no confusion is encountered.

Step-by-step explanation:

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