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Looks like a bug to me. I do get True for the following.

eq=tan(pi/5) == sin(pi/5)/cos(pi/5)
bool(eq.simplify_trig())

Note that eq.simplify_trig() gives:

4*sin(1/5*pi)/(sqrt(5) + 1) == 4*sin(1/5*pi)/(sqrt(5) + 1)