Two expressions are equal, but in GNU Octave it says thay are not equal, what is problem here?

Question

This is text from Octave comand prompt:

octave:7> power(cos(x/2),2)
ans = 0.9045
octave:8> (tan(x)+sin(x))/(2*tan(x))
ans = 0.9045
octave:9> power(cos(x/2),2)==(tan(x)+sin(x))/(2*tan(x))
ans = 0

Answer 1

https://floating-point-gui.de/

Answer 2

Mathematically speaking, the two functions are not the same:
the domain of the first is all R,
while the domain of the second excludes the points
x = pi/2+k*pi for all k in Z
Because of the tan(x) at the denominator

You could say the second is a restriction of the first

... Or it could be a floating-point approximation issue