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Summary of formulas that must be memorized in solving equations in junior high school mathematics
Many people pay more attention to solving equations in junior high school mathematics. I will sort them out for your reference.

Multiplication and factorization:

a2-b2=(a+b)(a-b)

a3+b3=(a+b)(a2-ab+b2)

a3-b3=(a-b)(a2+ab+b2)

Trigonometric inequality:

|a+b|≤|a|+|b|

|a-b|≤|a|+|b|

| a |≤b & lt; = & gt-b≤a≤b

|a-b|≥|a|-|b|-|a|≤a≤|a|

Solution of quadratic equation in one variable;

-b+√(B2-4ac)/2a-b-b+√(B2-4ac)/2a

Relationship between root and coefficient

X1+x2 =-b/ax1* x2 = c/a note: Vieta's theorem.

Discriminant b2-4a=0 Note: The equation has two equal real roots.

B2-4ac >0 Note: The equation has real roots.

B2-4ac & lt; 0 Note: The equation has multiple yokes.

Two angle sum formula:

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-sinBcosA

cos(A+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

tan(A+B)=(tanA+tanB)/( 1-tanA tanB)

tan(A-B)=(tanA-tanB)/( 1+tanA tanB)

ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)

ctg(A-B)=(ctgActgB+ 1)/(ctg b-ctgA)

Double angle formula:

tan2A=2tanA/( 1-tan2A)

ctg2A=(ctg2A- 1)/2ctga

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

Half-angle 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))

ctg(A/2)=√(( 1+cosA)/(( 1-cosA))

ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))

Sum-difference product:

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 = 2 sin((A+B)/2)cos((A-B)/2 cosa+cosB = 2 cos((A+B)/2)sin((A-B)/2)

tanA+tanB=sin(A+B)/cosAcosB

tanA-tanB=sin(A-B)/cosAcosB

ctgA+ctgBsin(A+B)/sinAsinB

-ctgA+ctgBsin(A+B)/sinAsinB

The sum of the first n terms of some series:

1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2

1+3+5+7+9+ 1 1+ 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: where r represents the radius of the circumscribed circle of a triangle.

Cosine theorem: b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..

The standard equation of a circle: (x-a)2+(y-b)2=r2 Note: (a, b) is the center coordinate.

General equation of circle: x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0

Parabolic standard equation: y2=2px

y2=-2px

x2=2py

x2=-2py

Side area of right-angle prism: S=c*h

Side area of oblique prism: S = c'* h

Side area of a regular pyramid: S= 1/2c*h'

Side area of prism: S = 1/2(c+c')h'

Area of frustum side: s =1/2 (c+c') l = pi (r+r) l.

Surface area of the ball: S=4pi*r2.

Area of cylinder side: s = c * h = 2pi * h

The lateral area of the cone: s =1/2 * c * l = pi * r * l.

Arc length formula: l=a*r, where a is the radian number of the central angle r >; 0

Sector 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: where s' is the straight cross-sectional area and l is the side length.

Cylinder volume formula: V=s*h

Cylinder: V=pi*r2h