Multiplication and factorization of common formulas in high school mathematics.

a2-B2 =(a+b)(a-b)a3+B3 =(a+b)(a2-a b+B2)a3-B3 =(a-b(a2+a b+B2).

Trigonometric inequality, a common formula in high school mathematics.

| a+b |≤| a |+| b | | a-b |≤| a |+| b | | a |≤b & lt； = & gt-b≤a≤b .

|a-b|≥|a|-|b|-|a|≤a≤|a| .

The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a.

The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.

Discriminations commonly used in high school mathematics.

B2-4ac=0 Note: This equation has two equal real roots.

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

B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.

The formula of trigonometric function, commonly used in high school mathematics.

Two-angle sum formula.

sin(A+B)= Sina cosb+cosa sin(A-B)= Sina cosb-sinb cosa .

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb .

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 = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA .

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

2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B).

2 cos acosb = cos(A+B)-sin(A-B)-2 sinasinb = 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)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb .

ctgA+ctgBsin(A+B)/sinAsinB .