Sum-difference product and difference product are mathematical formulas used to calculate trigonometric functions. The sum-difference product formula *** 10 group includes sine, cosine, tangent and cotangent, and it is a set of identities in trigonometric functions. When applying sum-difference product, it must be a trigonometric function with the same name. 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.
Sum-difference product formula
Sina+sin B = 2 sin[(a+β)/2]2 cos[(a-β)/2]；
Sina-sinβ= 2cos[(a+β)/2]sin[(a-β)/2]；
cosa+cosβ= 2 cos[(a+β)/2]2 cos[(a-β)/2]；
cosa-cosβ=-2 sin[(a+β)/2]sin[(a-β)/2]；
sinq 2 cosβ= 0.5[sin(a+β)+sin(a-β)]；
cosQ2sinβ=0。 5[sin(a+β)-sin(a-β)]；
cosa2 cos β =0。 5[cos(a+β)+cos(a-β)]；
sinQ2sinβ=-0。 5[cos(a+β)-cos(a-β)]；
Sum and difference product formula The memory formula and difference product need to have the same name,
Clearly remember variable substitution,
If the function has a different name,
Change the name of the complementary corner.
The abbreviation is:
S+S=2S。 c；
S-S=2C。 s；
C+C=2C。 c；
C-C =-2S●S；
For the product combination difference formula, the first principle is that if there are synonyms on the left side of the equal sign, the right side of the equal sign is all sin, the left side of the equal sign has the same name, and the right side of the equal sign is all cos. Secondly, the sum and difference in the middle of the right take the second term on the left. If cos is+,if sin is-,add a negative sign when remembering sin*sin. For the sum-difference product formula, first, if the left side of the equal sign is full of sin, the right side is synonymous; If the left side of the equal sign is full of cos, then the right side of the equal sign has the same name; Secondly, the middle symbol on the left of the equal sign determines the second item on the right; If it is positive, it is cos; if it is negative, it is sin; Then you can write a complete right formula according to the first principle; Finally, remember that cos-cos should add a negative sign.
In a triangle, the ratio of the sine of each side to its diagonal is equal, which is equal to the diameter of the circumscribed circle of the triangle. When a triangle is solved by sine theorem, its solution is unique. Because of the instability of triangle, its solution is uncertain. We can consider and solve the problem by combining the plane geometry drawing method, the theorem of big side to big angle, the theorem of big angle to big side and the theorem of triangle interior angle.
The above is the explanation of the basic knowledge about the sum-difference product formula. If you want to calculate sum and differential product simply and quickly, you must always remember the formula of sum and differential product.