How to decompose the sin(x)+cos(x) function into a Taylor series in C++ by overloading the operation of putting in the input stream and extracting from the output stream?

Faced with the following task: Implement a module whose connection overloads the operations of placing in the output stream and extracting from the input stream for a class containing methods for decomposing the sin(x)+cos(x) function into a Taylor series. The first n terms of the decomposition should be displayed on the screen. The value of n is determined by the user.

So far, I have implemented this program for sin(x). There is a problem in how to make a formula for the expansion of the function sin (x)+cos (x) in a series Taylor in C++. I searched all the sources on the Internet about this - the result is zero. I would be very grateful.

#include <iostream>
#include <cmath>

using namespace std;

class Node {
private:
    float x;
    int n;

public:
    Node();
    friend ostream& operator << (ostream&, const Node&);
    friend istream& operator >> (istream&, Node&);
};

Node::Node() {
    x = 0;
    n = 0;

}

istream& operator >> (istream& in, Node& tam) {
    cout << "Введите x: ";
    in >> tam.x;
    cout << "Введите n: ";
    in >> tam.n;
    return in;
}
ostream& operator << (ostream& out, const Node& tam) {
    float gh = 0.0;
    for (int st = 1; st <= tam.n; st++) {
        gh = exp((st*(log(tam.x)))) / st;
        gh = tam.x / st;
        out << "(" << gh << ")" << "+" << gh << "";
    }
    return out;
}

int main() {
    setlocale(LC_ALL, "Russian");
    Node tam;
    cin >> tam;
    cout << tam;
    system("pause");
    return 0;
}