题意：

给你一个长度为 $n$ 的序列 $a$ ，有 $m$ 次操作，每次操作分两种类型：

$(1) l, r, v$ ，将 $a_l,a_{l+1},...,a_r$ 分别加上 $v$ 。

$(2) l, r$ ，询问 $∑i=lrsin⁡(ai)\sum_{i=l}^r\sin(a_i)$ 。

思路：

闲的没事来水俩题。

考虑高中的和差公式， $s i n (a + b) = s i n (a) c o s (b) + s i n (b) c o s (a)$ ，所以我们可以多维护一个 $c o s$ ，让后 $c o s (a + b) = c o s (a) c o s (b) - s i n (x) s i n (b)$ ，打个 $l a z y$ ，维护的时候注意一下细节即可。

瞎搞维护一下就好。

// Problem: P6327 区间加区间sin和
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P6327
// Memory Limit: 125 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
//#pragma GCC optimize(2)
#include<cstdio>
#include<iostream>
#include<string>
#include<cstring>
#include<map>
#include<cmath>
#include<cctype>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include<sstream>
#include<ctime>
#include<cstdlib>
#include<random>
#include<cassert>
#define X first
#define Y second
#define L (u<<1)
#define R (u<<1|1)
#define pb push_back
#define mk make_pair
#define Mid ((tr[u].l+tr[u].r)>>1)
#define Len(u) (tr[u].r-tr[u].l+1)
#define random(a,b) ((a)+rand()%((b)-(a)+1))
#define db puts("---")
using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); }
//void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); }
//void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;const int N=200010,mod=1e9+7,INF=0x3f3f3f3f;
const double eps=1e-6;int n,m;
int a[N];
struct Node {int l,r;double sums,sumc;LL lazy;
}tr[N<<2];void pushup(int u) {tr[u].sumc=tr[L].sumc+tr[R].sumc;tr[u].sums=tr[L].sums+tr[R].sums;
}void pushdown(int u) {LL lazy=tr[u].lazy; tr[u].lazy=0;tr[L].lazy+=lazy; tr[R].lazy+=lazy;double ss=tr[L].sums,sc=tr[L].sumc;tr[L].sums=ss*cos(lazy)+sin(lazy)*sc;tr[L].sumc=sc*cos(lazy)-ss*sin(lazy);ss=tr[R].sums,sc=tr[R].sumc;tr[R].sums=ss*cos(lazy)+sin(lazy)*sc;tr[R].sumc=sc*cos(lazy)-ss*sin(lazy);
}void build(int u,int l,int r) {tr[u]={l,r};if(l==r) {tr[u].sums=sin(a[l]);tr[u].sumc=cos(a[l]);return;}build(L,l,Mid); build(R,Mid+1,r);pushup(u);
}void change(int u,int l,int r,int x) {if(tr[u].l>=l&&tr[u].r<=r) {tr[u].lazy+=x;double ss=tr[u].sums,sc=tr[u].sumc;tr[u].sums=ss*cos(x)+sin(x)*sc;tr[u].sumc=sc*cos(x)-sin(x)*ss;return;}pushdown(u);        if(l<=Mid) change(L,l,r,x);if(r>Mid) change(R,l,r,x);pushup(u);
}double query(int u,int l,int r) {if(tr[u].l>=l&&tr[u].r<=r) return tr[u].sums;pushdown(u);double ans=0.0;if(l<=Mid) ans+=query(L,l,r);if(r>Mid) ans+=query(R,l,r);return ans;
}int main()
{
//	ios::sync_with_stdio(false);
//	cin.tie(0);scanf("%d",&n);for(int i=1;i<=n;i++) scanf("%d",&a[i]);build(1,1,n);scanf("%d",&m);while(m--) {int op,l,r; scanf("%d%d%d",&op,&l,&r);if(op==1) {int x; scanf("%d",&x);change(1,l,r,x);} else printf("%.1lf\n",query(1,l,r));}return 0;
}
/**/