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Single variable derivative of expression (symbolic)

I wrote HTML code using JavaScript to distinguish one variable. My code is here . I used Mathjax to print the output. But the result is not simplified. For example, the derivative of is sin(x)/cos(x)obtained as

((((cos(x))*(cos(x)))-((sin(x))*(-(sin(x)))))/((cos(x))^2))

which can be simplified to

(sin(x)^2+cos(x)^2)/cos(x)^2

I built an expression tree using the Dijkstra shunt algorithm. And then built a derivative expression tree recursively. But I have a problem with simplification.

Can anyone help with product simplification? My knowledge is not related to elementary data structures.

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