For personal use only in study and research; not for commercial use
圆函数（三角函数）
1.基本性质：
tanx?sinxcosx,cotx?cosxsinx secx?1cosx,cscx?1sinx
tanxcotx?1
sinxcscx?1 secxcosx?1
sin2x?cos2x?1
1?tan2x?sec2x,1?cot2x?csc2x
2.奇偶性：
sin(?x)??sinx cos(?x)?cosx
tan(?x)??tanx
3.两角和差公式
sin(x?y)?sinxcosy?cosxsiny cos(x?y)?cosxcosysinxsiny
tan(x?y)?tanx?tany1tanxtany
4.二倍角公式
sin2x?2sinxcosxcos2x?cos2x?sin2x?2cos2x?1?1?2sin2xtanx2?2tanx1?ta2nx
双曲函数
1.基本性质：
thx?shxchx,cthx?chxshx
sechx?1chx,cschx?1shx
thxcthx?1 shxcschx?1 sechxchx?1
ch2x?sh2x?1
1?th2x?sech2x,1?cth2x??csch2x
2.奇偶性：
sh(?x)??shx ch(?x)?chx
th(?x)??thx
3.两角和差公式
sh(x?y)?shxchy?chxshy ch(x?y)?chxchy?shxshy
th(x?y)?thx?thy1?thxthy
4.二倍角公式
sh2x?2shxchx
ch2x?ch2x+sh2x?2ch2x?1 ?1?2sh2xth2x?2thx1?th2x
5.半角公式
sin2x1?cosx2x1?cosx2?2,cos2?2
tanx2?sinx1?cosx1?cosx?sinx
1?cosx?2sin2x2,1?cosx?2cos2x2
6.万能公式
2tanx1?xsinx?2tan2,cosx?21?tan2x1?tan2x 222tanxtanx?2 1?tan2x2
7.三倍角公式
sin3x?3sinx?4sin3xcos3x?4cos3x?3cosx
8.积化和差公式
sinxcosy?12??sin?x?y??sin?x?y???cosxsiny?12??sin?x?y??sin?x?y??? cosxcosy?12??cos?x?y??cos?x?y???sinxsiny??12??cos?x?y??cos?x?y???
9.和差化积公式
sinx?siny?2sinx?yx?y2cos2sinx?siny?2cosx?yx?y2sin2cosx?cosy?2cosx?yx?y2cos2cosx?cosy??2sinx?y2sinx?y2 5.半角公式
sh2x2?chx?12,ch2x2?chx?12
thxshxch2?x?1chx?1?shx
chx?1?2sh2x2,chx?1?2ch2x2
6.万能公式
2thxxshx?21?th2,cosx?21?th2x1?th2x 222thxthx?2 1?th2x2
7.三倍角公式
sh3x?3shx?4sh3x ch3x?4ch3x?3chx
8.积化和差公式
shxchy?12??sh?x?y??sh?x?y???chxshy?12??sh?x?y??sh?x?y??? chxchy?12??ch?x?y??ch?x?y???shxshy?12??ch?x?y??ch?x?y???
9.和差化积公式
shx?shy?2shx?yx?y2ch2shx?shy?2chx?yx?y2sh2chx?chy?2chx?yx?y2ch2 chx?chy?2shx?yx?ysh 22