Two-angle summation formula sin (a+b) = sinacosb+cosasinbsin (a-b) = sinacosb-sinbcosa.

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 = 2tana/(1-tan2a) ctg2a = (ctg2a-1)/2ctga cos2a = cos2a-sin2a = 2cos2a-1=1-2sin2a.

Half-angle formula sin (a/2) = √ ((kloc-0/-COSA)/2) sin (a/2) =-√ ((kloc-0/-COSA)/2) cos (a/2) = √ ((1+)

Sum and difference of 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)

Sum-difference product 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+ctgB=sin(A+B)/sinAsinB

-ctgA+ctgB=sin(A+B)/sinAsin

The concepts of set and function

I. Collection of related concepts

1, meaning of set: some specified objects are set together into a set, where each object is called an element.

2. Three characteristics of elements in a set:

1. element determinism; 2. Mutual anisotropy of elements; 3. The disorder of elements

Description: (1) For a given set, the elements in the set are certain, and any object is either an element of the given set or not.

(2) In any given set, any two elements are different objects. When the same object is contained in a set, it has only one element.

(3) The elements in the set are equal and have no order. So to judge whether two sets are the same, we only need to compare whether their elements are the same, and we don't need to examine whether the arrangement order is the same.

(4) The three characteristics of set elements make the set itself deterministic and holistic.

3. Expression of assembly: {…} such as {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean}

1.Set is expressed in Latin letters: a={ basketball player of our school}, b={ 1, 2, 3, 4, 5}

2. Representation methods of sets: enumeration and description.

Note: Commonly used number sets and their symbols:

The set of nonnegative integers (i.e. natural number set) is recorded as n.

Positive integer set n* or n+ integer set z rational number set q real number set r

On the concept of "belonging"

Elements in a collection are usually represented by lowercase Latin letters. For example, if A is an element of set A, it means that A belongs to set A, and it is marked as A ∈ A; On the contrary, if a does not belong to the set a, it is recorded as a(a

Enumeration: enumerate the elements in the collection one by one, and then enclose them in braces. Description: Describes the common attributes of the elements in the collection. A method of representing a set with braces. A method to indicate whether some objects belong to this set under certain conditions. ① Language description: Example: {a triangle that is not a right triangle} ② Mathematical expression description: Example: The solution set of inequality x-3]2 is {x(r| x-3]2} or {x| x-3]2} 4. Collection classification: 1. A finite set contains finite elements. 2. An infinite set contains infinite elements. 3. The empty set does not contain any elements. Example: {x|x2=-5} 2. The basic relationship between sets is 1. "Inclusion" Relation-Subset Note: There are two possibilities (1). (2)a and B are the same set. On the other hand, set A is not included in set B, or set B does not include set A, which is marked as ab or ba 2. "Equality" relation (5≥5 and 5≤5, then 5=5) Example: Let a = {x | x2- 1 = 0} b = {-. If any element of set A is an element of set B and any element of set B is an element of set A, we say that set A is equal to set B, that is, a=b ① Any set is a subset of itself. A(a ② proper subset: if a(b) and a( b), set A is the proper subset of set B, and if a(b) is marked as a (b, b(c or ba) ③. Then a (c4) If a(b and b(a then A = B 3), the set without any elements is called an empty set and recorded as φ. An empty set is a subset of any set, and an empty set is a proper subset of any non-empty set. 3. The operation of the set is 1. Definition of intersection: Generally, the set composed of all elements belonging to A and B is called A, and the intersection of B is marked as a∩b (pronounced as "A intersection with B"), that is, a∩b={x|x∈a, x∈b}. 2. Definition of union: Generally speaking, a set consisting of all elements belonging to set A or set B is called A and B. A ∩ B = B ∩ A, A ∪ A = A, A ∪ B = B ∪ A.4, complete set and complement set (1. Usually expressed by u. (3) Properties: (1) Cu (C UA) = A (C UA).