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]

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)]

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​)

4句口诀巧记【积化和差、和差化积】八个等式