Two-angle sum formula

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

Double angle formula

tan2A=2tanA/( 1-tan^2A)

cos2a=cos^2a-sin^2a=2cos2a- 1= 1-2sin2a

Sum difference product

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

2 cosa cosb = 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

cotA+cot bsin(A+B)/Sina sinb-cotA+cot bsin(A+B)/Sina sinb

Sine theorem a/sinA=b/sinB=c/sinC=2R.

Cosine theorem B2 = A2+C2-2accosb2 = A2+C2-2accosb2.

The standard equation of a circle (X-A) 2+(Y-B) 2 = R 2 Note: (A, B) is the center coordinate.

General equation of circle x 2+y 2+dx+ey+f = 0 note: d 2+e 2-4f > 0.

Parabolic standard equation y 2 = 2px y 2 =-2px x 2 = 2py x 2 =-2py.

Lateral area of a regular prism S=c*h lateral area of a regular pyramid s =1/2c * h.

The surface area of the sphere is s = 4 π r 2.

The area of cylinder side surface S=c*h=2π*h Arc length formula l=a*r a is the radian number of central angle r>0 Sector area formula s =1/2 * l * r.

Conical volume formula V= 1/3*S*H Conical volume formula V = 1/3 * π * r 2h

derivant

① C'=0(C is a constant function) ② (x n)' = NX (n-1) (n ∈ q *); Memorize the derivative ③ (sinx)' = cosx (cosx)' =-sinx (tanx)' =1(cosx) 2 = (secx) 2 =1+(tanx) 2-(cotton). ^2(secx)' = tanx secx(cscx)' =-cotx cscx(arcsinx)'= 1/( 1-x^2)^ 1/2(arccosx)'=- 1/( 1-x^2)^ 1/2(arctanx) ' = 1/( 1+x^2)(arccotx)'=- 1/( 1+x^2)(arcsecx)'= 1/(|x|(x^2- 1)^ 1/2)(arccscx)'=- 1/(|x| (x^2- 1)^ 1/2)④(sinhx)' = coshx(coshx)' = sinhx(tanhx)'= 1/(coshx)^2=(sechx)^2((sechx)' =-tanhx sechx(cschx) ' =-cothx cschx(arsinhx)' = 1/(x2+ 1 1)(arcothx)'= 1/(x^2- 1)(| x | > 1)(arse CHX)' = 1/(x( / Kloc-0/-x 2)1/2) (arcschx)' =1(x (1+x) =1/x (ln is a natural logarithm) (logax)' = x (.

vectors

Law of association: (λ a) b = λ (a b) = (a λ b). The distribution law λ+μ) a = λ a+μ a. The distribution law λ (a+b) = λ a+λ b. 。

a b=|a| |b| cosAFA .

A = | a | 2. a⊥b÷a b = 0

, ∣∣a∣-∣b∣∣≤∣a+b∣≤∣a∣+∣b∣ ① If and only if A and B are reversed, the left side is equal. ∣∣a∣-∣b∣∣≤∣a-b∣≤∣a∣+∣b∣。 ① If and only if the directions of A and B are the same, the left side takes the equal sign ② If and only if the directions of A and B are opposite, the right side takes the equal sign.

The formula for judging the center of gravity of triangle is in △ABC. If GA +GB +GC=O, then G is the center of gravity of △ABC.

Three-point * * line theorem If OC=λOA +μOB and λ+μ= 1, then A, B and C are three-point * * lines.

Necessary and Sufficient Conditions for Verticality of Vector

The necessary and sufficient condition for a⊥b is that a b = 0, that is, x 1x2+y 1y2=0.

Probability; possibility

Property 1. P (φ) = 0。 Characteristic 2 (limited additivity). When n events A 1, …, An are incompatible with each other: P(a 1∨). . ∪ an) = p (a 1)+...+p (an)。 Real estate 3. For any event, a: p (a) = 1-p (not a). Property 4. When events A and B satisfy that A is contained in B, P (b-a). P (a) ≤ 1。 Real estate 6. For any two events a and b, P (B-A) = P (B)-P (AB). Attribute 7 (addition formula). For any two events a and b, P (A ∪ B) = P (A)+P (.