Question

How to simplify (as in get rid of trig functions)? (tan+1(arccos(x)))^2

Answer 1

From Mathematica:
\[\text{ArcCos}[x]^2 \text{Tan}[1]^2=-\frac{\left(e^{-i}-e^i\right)^2 \left(\frac{\pi }{2}+i \text{Log}\left[i x+\sqrt{1-x^2}\right]\right)^2}{\left(e^{-i}+e^i\right)^2} \]