判别式 b2-4ac=0注：方程有两个相等的实根 b2-4ac>0注：方程有两个不等的实根 b2-4ac<0注：方程没有实根，有共轭复数根<>
a2-b2=(a b)(a-b)a3 b3=(a b)(a2-ab b2)a3-b3=(a-b(a2 ab b2)
|a b|≤|a| |b||a-b|≤|a| |b||a|≤b<=>-b≤a≤b
-b √(b2-4ac)/2a-b-√(b2-4ac)/2a
X1 X2=-b/aX1__X2=c/a注：韦达定理
b2-4ac<0注：方程没有实根，有共轭复数根<>
sin(A B)=sinAcosB cosAsinBsin(A-B)=sinAcosB-sinBcosA
cos(A B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB sinAsinB
tan(A B)=(tanA tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1 tanAtanB)
ctg(A B)=(ctgActgB-1)/(ctgB ctgA)ctg(A-B)=(ctgActgB 1)/(ctgB-ctgA)
tan2A=2tanA/(1-tan2A)ctg2A=(ctg2A-1)/2ctga
cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a
sin(A/2)=√((1-cosA)/2)sin(A/2)=-√((1-cosA)/2)
cos(A/2)=√((1 cosA)/2)cos(A/2)=-√((1 cosA)/2)
tan(A/2)=√((1-cosA)/((1 cosA))tan(A/2)=-√((1-cosA)/((1 cosA))
ctg(A/2)=√((1 cosA)/((1-cosA))ctg(A/2)=-√((1 cosA)/((1-cosA)
2sinAcosB=sin(A B) sin(A-B)2cosAsinB=sin(A B)-sin(A-B)
2cosAcosB=cos(A B)-sin(A-B)-2sinAsinB=cos(A B)-cos(A-B)
sinA sinB=2sin((A B)/2)cos((A-B)/2cosA cosB=2cos((A B)/2)sin((A-B)/2)
tanA tanB=sin(A B)/cosAcosBtanA-tanB=sin(A-B)/cosAcosB
ctgA ctgBsin(A B)/sinAsinB-ctgA ctgBsin(A B)/sinAsinB
1 2 3 4 5 6 7 8 9 … n=n(n 1)/21 3 5 7 9 11 13 15 … (2n-1)=n2
2 4 6 8 10 12 14 … (2n)=n(n 1)12 22 32 42 52 62 72 82 … n2=n(n 1)(2n 1)/6
13 23 33 43 53 63 …n3=n2(n 1)2/41__2 2__3 3__4 4__5 5__6 6__7 … n(n 1)=n(n 1)(n 2)/3
