1, average inequality: a+b≥2√ab(a≥0, b≥0), this formula is also called inequality of arithmetic average and geometric average. It shows that for any real numbers A and B, their sum a+b is at least equal to their geometric mean 2√ab. If and only if a=b, the equal sign holds. This formula is very useful in solving the maximum problem and can be used to determine the minimum value of some functions.

2. Trigonometric function and differential angle formula: sin(a+b)=sinacosb+cosasinb, cos(a+b)=cosacosb-sinasinb. These two formulas can be used for complex trigonometric function calculation, and the unknown trigonometric function value can be obtained through the known trigonometric function value. For example, given the values of sin a and cos b, the values of sin(a+b) and cos(a+b) can be obtained.

3. Sum formula of arithmetic sequence: n/2*(a 1+an), which can quickly calculate the sum of the first n items in arithmetic progression. Where a 1 stands for the first term, an stands for the nth term, and n stands for the number of terms. For example, if the first term of a arithmetic progression is 2, the fifth term is 10, and the number of terms is 10, then the sum of the first 10 terms is 5*(2+ 10)=60.

4. The formula of the distance between two points: √((x 1-x2)? +(y 1-y2)？ ), this formula can be used to calculate the distance between two points on the plane. Where (x 1, y 1) and (x2, y2) respectively represent the abscissa and ordinate of two points. For example, if the coordinates of two points are (1, 2) and (4, 5) respectively, then the distance between them is √ (1-4)? +(2-5)? )=5。

The function of mathematical formula:

1, Simplify calculation: You can use mathematical formulas to simplify the complicated calculation process and make the calculation simple and fast. For example, the square difference formula can quickly solve the square difference problem.

2. Connecting variables: Mathematical formulas can connect different variables and establish mathematical relationships between variables. For example, the linear relationship between two variables can be expressed in mathematical form by using the solution formula of linear equation.

3. Inference conclusion: The conclusion can be deduced by mathematical formula, and a new conclusion can be obtained through the deformation and expansion of the known formula. For example, the formula of trigonometric function can be used to deduce the values and relationships of various trigonometric functions.

4. Problem solving: Mathematical formulas can be used to solve various practical problems, such as calculating the probability of events with probability formulas and calculating the area and volume of graphs with geometric formulas.

5. Discovering laws: Mathematical formulas can help people discover mathematical laws and phenomena. By observing and analyzing known formulas, new laws and properties can be discovered.