I show to my sdudents the equations sin a + sin a = tan a
99% say that it is not correct? But 1%...
Your text "sin(a)+sin(a)=tan(a)" shows different from you mathcad sheet picture.
Because it's more intrigueing I tried the latter first:
Note that there are four primary solutions to this problem. (see the float results). I expanded the smallest real solution up to 2 of 5 pages..
I guess the size is the reason why Prime will not give you the symbolic result...?
In Mathcad 15 all symbolic results are equally wide ("only" three page widths). Using the modifier "simplify,max" the result gets four pages width.
So I guess the picture you posted in your initial post does not show a bug or failure - it shows a hyperbolic triangle with three 30° angles (with a defect of pi/2).
The failure or bug is not the picture but your assumption that the angles would add up to 180° (which the angles in a hyperbolic triangle never do and which is not claimed in the picture) 😉
BTW, the picture is a stock picture and sells with different persons in different poses:
Its a long time since the artist went to school and learned math.