Commonly used mathematical formulas
1, multiplication and factorization a2-B2 = (a+b) (a-b) a3+B3 = (a+b) (a2-ab+B2) a3-B3 = (a-b (a2+ab+B2))
2. Trigonometric inequality | A+B |≤| A |+B ||||||| A |+B|| A |≤ B < = >-B≤ A ≤ B | A-B |≥| A |-B| | A |≤
3. The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a.
4. the relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a note: Vieta theorem discriminant b2-4ac=0 note: the equation has two equal real roots B2-4ac > 0 note: the equation has two unequal real roots B2-4ac < 0 note:
5. The formula of the sum of two angles of trigonometric function
6、sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinBcosA
7、cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
8、tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
9、ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
10, angle doubling formula tan2a = 2tana/(1-tan2a) ctg2a = (ctg2a-1)/2ctga.
Mathematical key formula
1 1、cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
12, and the half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((1-COSA)/2).
13、cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
14、tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
15、ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum-difference product 16, 2sinacosb = sin (a+b)+sin (a-b) 2cosasinb = sin (a+b)-sin (a-b).
17、2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
18、sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
19 、+ tanB = sin(A+B)/cosAcosB tanA-tanB = sin(A-B)/cosAcosB
20、ctgA+ctgBsin(A+B)/Sina sin B-ctgA+ctgBsin(A+B)/Sina sinb
Knowledge points that junior high school students must master
1 There is only one straight line at two points.
The line segment between two points is the shortest.
The complementary angles of the same angle or equal angle are equal.
The complementary angles of the same angle or the same angle are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7 Parallel axiom passes through a point outside a straight line, and there is only one straight line parallel to this straight line.
If both lines are parallel to the third line, the two lines are also parallel to each other.
The same angle is equal and two straight lines are parallel.
The internal dislocation angles of 10 are equal, and the two straight lines are parallel.
1 1 are complementary and two straight lines are parallel.
12 Two straight lines are parallel and have the same angle.
13 two straight lines are parallel, and the internal dislocation angles are equal.
14 Two straight lines are parallel and complementary.
Theorem 15 The sum of two sides of a triangle is greater than the third side.
16 infers that the difference between two sides of a triangle is smaller than the third side.
The sum of the internal angles of 17 triangle is equal to 180.
The above are all the formulas of junior high school mathematics that I summarized for you, for reference only, and I hope it will help you.