We add the two formulas to get sin(A+B)+sin(A-B)=2sinA*cosB, so sinA*cosB=sin (A+B) +sin(A-B) is the same. If you subtract the two formulas, you can get COSA SINB = (SIN (A+B)-SIN (.
Cos(A+B)=cosA*cosB-sinA*sinB, COSA (a-b) = COSA * COSB+SINA * SINB can be obtained by the cosine formula of the sum and difference of two angles. Adding the two formulas, we can get cos(A+B)+cos(A-B)=2cosA*cosB.
Sum-difference product formula: including sine, cosine, tangent, cotangent and difference product formula, which is a set of identities in trigonometric function, and sum-difference product formula *** 10 group. When sum-difference product is applied, it must be a trigonometric function with the same name (except tangent cotangent). If it is a synonym, it must be formulated into the same name by induction; If it is a high-order function, it must be reduced once by the power reduction formula.
No matter sine function or cosine function, only the sum and difference of trigonometric functions with the same name can be converted into products. This is mainly based on proof memory, because if it is not a trigonometric function with the same name, the product term of the sum and difference formula of two angles will have different forms, so there will be no cancellation and the same term, and it is impossible to simplify it.
The benefits of learning mathematics:
1. Mathematics can cultivate people's integrity and honesty. Mathematics pays the most attention to convincing people by reasoning, and only believes in the results of logical reasoning.
Mathematics can cultivate people's tenacity and courage. The great math educator Paulia said: "Difficulties and problems belong to the same concept. If there is no difficulty, there will be no problem.
3. Mathematics can cultivate people's overall consciousness. To solve mathematical problems, we must comprehensively consider the problems from the known to the conclusion and grasp the interrelationships of all aspects. Mathematics teaching can cultivate students to consider problems comprehensively from the overall situation.
Mathematics can cultivate people's good character. The better a person's math study, the more flexible his thinking. In this case, his enthusiasm and enthusiasm are very high, and he is good at expressing his ideas and methods, so that his communication skills will be tempered and his self-confidence will be gradually enhanced.