#include <iostream>

using namespace std;

void cout_a(int m,int n){
    if(m==n) cout<<"sin("<<n<<")";
    else{
        cout<<"sin("<<m<<"+";
        cout_a(m+1,n);
        cout<<")";
    }
}

void cout_s(int m,int n){
    if(m==1){
        cout_a(1,1);
        cout<<"+"<<n;
    }
    else{
        cout<<"(";
        cout_s(m-1,n);
        cout<<")";
        cout_a(1,m);
        cout<<"+"<<n+1-m;
    }
}

int main(void){
    int n;
    cin>>n;
    cout_s(n,n);
    cout<<endl;
    return 0;
}

I know.I am using GB2312.So I see -s as &#8211;s.
The following is the AC code.

#include <iostream>

using namespace std;

void cout_a(int m,int n){
    if(m==n) cout<<"sin("<<n<<")";
    else{
        cout<<"sin("<<m;
        if(m%2==1) cout<<"-";
        else cout<<"+";
        cout_a(m+1,n);
        cout<<")";
    }
}

void cout_s(int m,int n){
    if(m==1){
        cout_a(1,1);
        cout<<"+"<<n;
    }
    else{
        cout<<"(";
        cout_s(m-1,n);
        cout<<")";
        cout_a(1,m);
        cout<<"+"<<n+1-m;
    }
}

int main(void){
    int n;
    cin>>n;
    cout_s(n,n);
    cout<<endl;
    return 0;
}