How to plot the imaginary part of $\tan(x)^{\cos(x)}$ on the $xy$-plane?

Question

So recently, I asked this question on Math.SE on if my thought process on how to solve the limit $\lim_{x\to(\pi/2)^-}\tan(x)^{\cos(x)}$ was correct, and actually, while I was solving this, I was trying to plot the imaginary part of said equation in Mathematica for practice.

I do have code for plotting the real-value part

Plot[Tan[x]^Cos[x],{x,-5,5}]

which does work as intended, however I'm confused as to how to get the imaginary plot of this function.

I have tried using

ComplexPlot[Tan[x]^Cos[x],{x,-5,5}]

but it returns the following errors:

ComplexPlot: Corners for x in {x,-5,5} must have distinct machine-precision real and imaginary parts.
ComplexPlot: Corners for x in {x,-5,5} must have distinct machine-precision real and imaginary parts.
ComplexPlot: Corners for x in {x,-5,5} must have distinct machine-precision real and imaginary parts.
General: Further output of ComplexPlot::plld will be suppressed during this calculation.
ComplexPlot: Corners for x in {x,-5,5} must have distinct machine-precision real and imaginary parts.
ComplexPlot: Corners for x in {x,-5,5} must have distinct machine-precision real and imaginary parts.
Out[6]= ComplexPlot[Tan[x]^Cos[x],{x,-5,5}]

I managed to fix this by adding an imaginary part to my bounds (my current code so far)

ComplexPlot[Tan[x]^Cos[x],{x,-5-5i,5+5i}]

which returns this

which looks cool, but it's not what I'm trying to do.

What I'm trying to do is this is plot the imaginary part of $\tan(x)^{\cos(x)}$ on the $xy$-plane like this (ignore the blue line):

although I don't know how to fix my code from here. So my question is:

How do I plot the imaginary part of $\tan(x)^{\cos(x)}$ on the $xy$-plane?

Answer 1

Plot[Evaluate[ReIm[Tan[x]^Cos[x]]], {x, -5, 5}, 
 PlotRange -> {All, {-5, 5}}]

Answer 2

Since V 12.0 there is ReImPlot

ReImPlot[Tan[x]^Cos[x], {x, -5, 5},
 GridLines -> Automatic,
 PlotLegends -> {"Expressions", "ReIm"},
 PlotRange -> {All, {-5, 5}}]

We also have AbsArgPlot which generates a plot of Abs[f] colored by Arg[f]

AbsArgPlot[Tan[x]^Cos[x], {x, -5, 5},
 Epilog ->
  {Dashed,
   {InfiniteLine[{Pi, 0}, {Pi, 1000}],
    InfiniteLine[{-Pi, 0}, {-Pi, 1000}]}},
 GridLines -> Automatic,
 PlotLegends -> Automatic]