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关于两个三角函数的和、差化积,已有公式直接应用。对于常用的正弦函数或余弦函数的三项和或四项和化积,虽然没有固定公式,但在某些特殊情况下,仍有规律可循。本文给出正弦函数与余弦函数三项和与四项和化积的一些充分条件,使得我们易于找出第一次用二项和化积公式后,有公因式可提,从而便于进一步把三角函数的和、差化成积的形式。命题1 若 1/2(α±β)=γ,则cosα+cosβ+cosγ必能化成积。证明设 1/2(α+β)=γ,则 cosα+cosβ+cosγ=2cos1/2(α+β)cos1/2(α-β)+cosγ
With regard to the sum and difference products of the two trigonometric functions, the existing formula has been applied directly. Although there are no fixed formulas for the generalized sine function or cosine function, there are still rules to follow in some special cases. In this paper, some sufficient conditions for the summation of the sum of the three terms of the sine function and the cosine function and the sum of the four terms and the summation product are given. This makes it easy for us to find out that the first use of the binomial sum formula and the common factor can be mentioned. The sum and difference of trigonometric functions are converted into the product form. Proposition 1 If 1/2(α±β)=γ, then cosα+cosβ+cosγ must be converted into a product. Proof Let 1/2(α+β)=γ, then cosα+cosβ+cosγ=2cos1/2(α+β)cos1/2(α-β)+cosγ