1、2sinAcosB=sin(A+B)+sin(A-B).

2、tan(A+B)=(tanA+tanB)/( 1-tanA tanB)。

3、cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a .

4、tan(A-B)=(tanA-tanB)/( 1+tanA tanB)。

5 、-ctgA+ctgBsin(A+B)/sinAsinB .

Mathematical compulsory one formula induction:

I. Operation of Exponent and Exponential Power

1, the concept of radical: generally speaking, if, then it is called n-th root, where >; 1 and ∈ *.

When it is an odd number, the power root of a positive number is a positive number and the power root of a negative number is a negative number. At this point, the power root of is represented by a symbol. The formula is called radical, here is called radical component, and here is called radical.

When it is an even number, a positive number has two power roots, and the two numbers are opposite. At this time, the positive power roots of positive numbers are represented by symbols, and the negative power roots are represented by symbols. Positive and negative power roots can be combined into +(>: 0). It can be concluded that negative numbers have no even roots; Any power root of 0 is 0, which is recorded as.

Note: When it is odd, it is even.

2. The power of the fractional exponent.

The meaning of the power of positive fraction index stipulates that the power of positive fraction index is equal to 0, and the power of negative fraction index is meaningless.

It is pointed out that after defining the meaning of fractional exponent power, the concept of exponent is extended from integer exponent to rational exponent, and the operational nature of integer exponent power can also be extended to rational exponent power.

3. The operational properties of exponential powers of real numbers.