Compare two equations in Maple

Question

Do any of you know how to compare alternative forms of equations in maple? No matter of what maple says false when I try to compare my two equations but I know they are the same.

\begin{align*} f(x) &= \frac{\sqrt{3}}{4} - \frac{3}{2}x^{2} + 100x\\ g(x) &= x\left(100-\frac{3}{2}x\right) + \frac{1}{2}x^{2}\sin(60^{\circ}) \end{align*}

I've tried

is(f(x)=g(x))
evalb(f(x)=g(x))

so far so good, but both report false while I know they are the same equations and wolfrom also reports true.

Answer 1

hint

replace $\sin (60) $ by $\sin (\frac \pi 3) $

and

add $x*x $ after $\sqrt {3} $ in the expression of $f (x) $ and try

simplify $ (f (x)-g (x));$

you should get $0$.

Answer 2

You are going to get the difference to be zero because your both equations/functions are not the same.

restart:
f:=(x)->sqrt(3)/4-3/2*x^2+100*x;
g:=(x)->x*(100-3/2*x)+1/2*x^2*sin(60);
f(x)-g(x);
evalf(simplify(%));

0.1524053106 $x^2$ + 0.4330127020