口诀1（基础）：先α后β，先加后减。
口诀2：异s同c【补充记忆：前加后减，双s双减】
s c = 1 2 [ s + s ] c c = 1 2 [ c + c ] sc=\frac{1}{2}[s+s]\ \ \ \ \ \ \ \ \ \ cc=\frac{1}{2}[c+c] sc=21[s+s] cc=21[c+c]
c s = 1 2 [ s − s ] s s = − 1 2 [ c − c ] cs=\frac{1}{2}[s-s]\ \ \ \ \ \ \ \ \ \ \ ss=-\frac{1}{2}[c-c] cs=21[s−s] ss=−21[c−c]
口诀3：积化和差内不除
s i n α c o s β = 1 2 [ s i n ( α + β ) + s i n ( α − β ) ] c o s α c o s β = 1 2 [ c o s ( α + β ) + c o s ( α − β ) ] sinαcosβ=\frac{1}{2}[sin(α+β)+sin(α-β)]\ \ \ \ \ \ \ \ \ \ cosαcosβ=\frac{1}{2}[cos(α+β)+cos(α-β)] sinαcosβ=21[sin(α+β)+sin(α−β)] cosαcosβ=21[cos(α+β)+cos(α−β)]
c o s α s i n β = 1 2 [ s i n ( α + β ) − s i n ( α − β ) ] s i n α s i n β = − 1 2 [ c o s ( α + β ) − c o s ( α − β ) ] cosαsinβ=\frac{1}{2}[sin(α+β)-sin(α-β)]\ \ \ \ \ \ \ \ \ \ sinαsinβ=-\frac{1}{2}[cos(α+β)-cos(α-β)] cosαsinβ=21[sin(α+β)−sin(α−β)] sinαsinβ=−21[cos(α+β)−cos(α−β)]
口诀4：和差化积内除2
s i n α + s i n β = 2 s i n ( α + β 2 ) c o s ( α − β 2 ) c o s α + c o s β = 2 c o s ( α + β 2 ) c o s ( α − β 2 ) sinα+sinβ=2sin(\frac{α+β}{2})cos(\frac{α-β}{2})\ \ \ \ \ \ \ \ \ \ cosα+cosβ=2cos(\frac{α+β}{2})cos(\frac{α-β}{2}) sinα+sinβ=2sin(2α+β)cos(2α−β) cosα+cosβ=2cos(2α+β)cos(2α−β)
s i n α − s i n β = 2 c o s ( α + β 2 ) s i n ( α − β 2 ) c o s α − c o s β = − 2 s i n ( α + β 2 ) s i n ( α − β 2 ) sinα-sinβ=2cos(\frac{α+β}{2})sin(\frac{α-β}{2})\ \ \ \ \ \ \ \ \ \ cosα-cosβ=-2sin(\frac{α+β}{2})sin(\frac{α-β}{2}) sinα−sinβ=2cos(2α+β)sin(2α−β) cosα−cosβ=−2sin(2α+β)sin(2α−β)
 泛型)
、filter()和reduce()函数)
![[书生·浦语大模型实战营]——第三节：茴香豆：搭建你的 RAG 智能助理](http://pic.xiahunao.cn/[书生·浦语大模型实战营]——第三节：茴香豆：搭建你的 RAG 智能助理)
