What is the content of the sum difference product formula? and what is the formula for the product o

1. Formula for Accumulation and Difference:

sin sin =- [cos( +cos( -cos cos = [cos( +cos( -sin cos = [sin( +sin( -cos sin = [sin( +sin( -2, and the difference product formula.

sinθ+sinφ=2sin cos

sinθ-sinφ=2cos sin

cosθ+cosφ=2cos cos

cosθ-cosφ=-2sin sin

The sum and difference product formula is the inverse form of the product and difference formula, and it should be noted that:

The first two formulas can be combined into one: sin +sin =2sincos is derived from the idea of "solving the system of equations", and the formula of the difference product is derived from the idea of "commutation".

Only the sum and difference of the function with the same name with the same absolute value of the coefficient can be directly formulated into the product, if the sum or difference of a sine and a cosine is used, the function of the same name should be formulated with the induction formula first, and then the product of the formula should be used.

The unity deformation is also a kind of sum difference product.

The sum and difference product of trigonometric functions can be understood as factorization in algebra, so what role does factorization play in algebra, and what role does the sum product formula play in trigonomy.

The formula for the sum difference is as follows: sin +sin =2sin[( 2]cos[( 2] sin -sin =2cos[( 2]sin[( Qidou2] cos +cos =2cos[( 2]cos[( 2] cos -cos =-2sin[( 2]sin[( 2]sin[( 2](x-y)].

sina＋sinb=2sin[(a＋b)/2]cos[(a－b)/2]

Proof: sina=sin[(a b) 2 (a b) 2]=sin[(a b) 2]cos[(a b) 2] cos[(a b) 2]sin[(a b) 2].

sinb=sin[(a＋b)/2－(a－b)/2]=sin[(a＋b)/2]cos[(a－b)/2]－cos[(a＋b)/2]sin[(a－b)/2]

Add the two formulas to get:

sina＋sinb=2sin[(a＋b)/2]cos[(a－b)/2]

Several other formulas are similar, mainly using the transformation of angles:

a=[(a＋b)/2]＋[a－b)/2]

b=[(a＋b)/2]－[a－b)/2]

and the difference product formulas, respectively:

and differential product of the common with the formula

The sum and argument dispersion product formulas, including sine, cosine, tangent and cotangent, are a set of identities in trigonometric functions, and there are 10 sets of sum difference product formulas. When applying the sum and differential products, it must be a trigonometric function of the same name (tangent and coward) for it to be implemented.

If it is a different name, it must be formulated with an induction formula to have the same name; If it is a higher-order Yunkai function, it must be reduced to one time using the power-reduction formula.

The sum difference product formula, including the sum and difference aging product formulas for sine, cosine, and tangent, is a set of identities in trigonometric functions.

Sine. sin +sin =2sin[( 2]·cos[( Lao Jin2]sin -sin =2cos[( 2]·sin[(2]cosine. cos +cos = 2cos[( 2]·cos[( 2]cos -cos =-2sin[( 2]·sin[(2]· sin[(2]tangent (variant with cotangent).

tan tan = sin( cos ·cos )cot cot =sin( potato liter ( sin ·sin )tan +cot =cos( -cos ·sin )tan -cot =-cos( +cos ·sin )

The formula for the sum of products is:sin cos = [sin( +sin( -2cos sin =sin( +sin( -2sin sin = [cos( -cos( +cos( +cos( +cos( -2cos( -2 and differential product elimination and the derivation of the formula of the difference sum are very simple.

sin( +sin( -cos( +cos( -This is the most basic trigonometric formula, and you can easily grasp the derivation of 8 formulas.

and the difference product formula.

sin sin 2sin( 2·cos( rough bridge potato ) 2sin sin 2cos( 2·sin( rocker 2cos cos 2cos( 2·cos( 2cos cos 2sin( 2·sin( 2