Common formulas for factorization
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).
Inductive formula of trigonometric function
Inductive formula 1: The values of the same trigonometric function of angles with the same terminal edges are equal.
Let α be an arbitrary acute angle, and the expression of this angle in the arc system.
sin(2kπ+α)=sinα(k∈Z).
cos(2kπ+α)=cosα(k∈Z).
tan(2kπ+α)=tanα(k∈Z).
cot(2kπ+α)=cotα(k∈Z).
Induce Formula 2: The relationship between the trigonometric function value of π+α and the trigonometric function value of α.
Let α be an arbitrary angle, and the expression of this angle in the arc system.
sin(π+α)=-sinα.
cos(π+α)=-cosα.
tan(π+α)=tanα.
cot(π+α)=cotα.
Inductive formula 3: the relationship between trigonometric function value of arbitrary angle α and-α.
sin(-α)=-sinα.
cos(-α)=cosα.
tan(-α)=-tanα.
cot(-α)=-cotα.
Inductive Formula 4: The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3.
sin(π-α)=sinα.
cos(π-α)=-cosα.
tan(π-α)=-tanα.
cot(π-α)=-cotα.
Inductive Formula 5: Using Formula 1 and Formula 3, we can get the relationship between the trigonometric function value of 2π-α and α.
sin(2π-α)=-sinα.
cos(2π-α)=cosα.
tan(2π-α)=-tanα.
cot(2π-α)=-cotα.
Induce Formula 6: The relationship between π/2α and the trigonometric function value of α.
sin(π/2+α)=cosα.
cos(π/2+α)=-sinα.
tan(π/2+α)=-cotα.
cot(π/2+α)=-tanα.
sin(π/2-α)=cosα.
cos(π/2-α)=sinα.
tan(π/2-α)=cotα.
cot(π/2-α)=tanα.
sin(3π/2+α)=-cosα.
cos(3π/2+α)=sinα.
tan(3π/2+α)=-cotα.
cot(3π/2+α)=-tanα.
sin(3π/2-α)=-cosα.
cos(3π/2-α)=-sinα.
tan(3π/2-α)=cotα.
cot(3π/2-α)=tanα.