1, square difference formula: a? -B? =(a+b)(a-b).

2. Complete square formula: a? +2ab+b？ =(a+b)？ .

3. Cubic sum formula: A? +b？ =(a+b)(a？ -ab+b？ )。

4. Cubic difference formula: a? -B? =(a-b)(a？ +ab+b？ )。

5. Complete cubic sum formula: a? +3a？ b+3ab？ +b？ =(a+b)？ .

6. Complete cubic difference formula: a? -3a？ b+3ab？ -B? =(a-b)？ .

7. Three complete square formulas: A? +b？ +c？ +2ab+2bc+2ac=(a+b+c)？ .

8. the formula of cubic sum of three terms: a? +b？ +c？ -3abc=(a+b+c)(a？ +b？ +c？ -ab-bc-ac).

Second, formulas of trigonometric functions.

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).

Three, the double angle formula

tan2A=2tanA/( 1-tan2A).

ctg2A=(ctg2A- 1)/2ctga .

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

Fourth, the 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))。

Verb (abbreviation for verb) and product of difference

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 = 2cos((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 .

Six, triangle inequality

|a+b|≤|a|+|b| .

|a-b|≤|a|+|b| .

| a |≤b & lt； = & gt-b≤a≤b .

|a-b|≥|a|-|b| .

-|a|≤a≤|a| .

Seven, graphic area formula

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

Side area of oblique prism: s = c' * h.

The 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.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.