Common mathematical formulas

Formula Classification	Formula expression
Multiplication and factorization	A2-b2 = (a + B) (a-B)	A3 + B3 = (a + B) (a2-ab + b2)	A3-b3 = (a-B) (A2 + AB + b2)
Triangle Inequality	| A + B | ≤ | A | + | B |	| A-B | ≤ | A | + | B |	| A | ≤ B <=>-B ≤ A ≤ B
	| A-B | ≥| A |-| B |	-| A | ≤ A ≤ | A |
Solution of a quadratic equation	[-B + √ (b2-4ac)]/2a	[-B-√ (b2-4ac)]/2a
Relationship between root and Coefficient	X1 + X2 =-B/	X1 * X2 = C/	Note: Verda Theorem
Discriminant	B2-4a = 0		Note: The equation has two solid roots equal to each other.
	B2-4ac> 0		Note: The equation has a solid root.
	B2-4ac		Note: The equation has a bounded plural root.
Trigonometric function formula
Two corners and Formula	Sin(A + B) =SinACosB +CosASinB		SinA-B =SinACosB-SinBCosA
	Cos(A + B) =CosACosB-SinASinB		CosA-B =CosACosB +SinASinB
	Tan(A + B) = (TanA +TanB)/(1-TanATanB)		Tan(A-B) = (TanA-TanB)/(1 +TanATanB)
	Cot(A + B) = (CotACotB-1 )/(CotB +CotA)		Cot(A-B) = (CotACotB + 1 )/(CotB-CotA)
Angle X formula	Tan2a = 2TanA/(1-Tan2a)		Cot2a = (Cot2a-1)/2CotA
	Cos2a =Cos2a-Sin2a = 2Cos2a-1 = 1-2Sin2a
Halfwidth Formula	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 ))
	Cot(A/2) = √ (1 +CosA)/(1-CosA ))		Cot(A/2) =-√ (1 +CosA)/(1-CosA ))
And difference Product	2SinACosB =Sin(A + B) +SinA-B)		2CosASinB =Sin(A + B )-SinA-B)
	2CosACosB =Cos(A + B )-SinA-B)		-2SinASinB =Cos(A + B )-CosA-B)
	SinA +SinB = 2Sin(A + B)/2)Cos(A-B)/2		CosA +CosB = 2Cos(A + B)/2)Sin(A-B)/2)
	TanA +TanB =Sin(A + B )/CosACosB		TanA-TanB =Sin(A-B )/CosACosB
	CotA +CotB =Sin(A + B )/SinASinB		-CotA +CotB =Sin(A + B )/SinASinB
The first n of some columns and	1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +... + N = n (n + 1)/2		1 + 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) 2/4		1*2 + 2*3 + 3*4 + 4*5 + 5*6 + 6*7 +... + N (n + 1) = n (n + 1) (N + 2)/3
Sine Theorem	A/SinA = B/SinB = C/SinC = 2R		Note: R indicates the outer circle radius of the triangle.
Cosine theorem	B2 = a2 + c2-2ac *CosB		Note: angle B is the angle between side A and side C.
Standard equation of a circle	(X-A) 2 + (Y-B) 2 = R2		Note: (A, B) is the Center Coordinate
General Equation of a circle	X2 + y2 + dx + ey + f = 0		Note: D2 + E2-4F> 0
Parabolic standard equation	Y2 = 2px	Y2 =-2px	X2 = 2py	X2 =-2py
Horizontal Bar Area	S = C * H	Oblique prism side area	S = C' * H
Cube side area	S = 1/2C * H'	Area of the right-side table	S = 1/2 (C + C') H'
Side area of the yutai	S = 1/2 (C + C') L = Pi (R + r) L	Ball Surface Area	S = 4pi * r2
Cylindrical side area	S = C * H = 2PI * H	Cone side area	S = 1/2 * C * l = pI * r * l
Arc Length Formula	L = A * R	A is the radians of the center ANGLE r> 0	Slice area formula	S = 1/2 * l * R
Cone volume Formula	V = 1/3 * S * H	Cone volume Formula	V = 1/3 * pI * r2h
Oblique prism volume	V = S' L		Note: Here, s' is the area of the straight section, and L is the side rib length.
Cylindrical volume Formula	V = S * H	Cylinder	V = pI * r2h