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定义在三角中,称式子f(π/2-x,π/2-y,π/2-z,…)为f(x,y,z,…)的三角对偶式。本文中我们用h(x,y,z,…)表示f(x,y,z,…)的三角对偶式。显然,f(x,y,z,…)也是h(x,y,x,…)的三角对偶式。例如sinx是cosx的三角对偶式;cos(x+y)是-cos(x+y)的三角对偶式;sinx+cosy是cosx+siny的三角对偶式。构造f(x,y,z,…)的三角对偶式h(x,y,z,…),利用f与h的加或减、乘、除、复数等运算,能使许多三角题的求解更为简炼。同时,构造一个三角题的对偶式,为编拟新的三角题提供了一个重要方法。
Defined in a triangle, the formula f (π/2-x, π/2-y, π/2-z, ...) is a triangular dual of f(x,y,z,...). In this paper, we use h(x,y,z,...) to represent the triangular dual of f(x,y,z,...). Obviously, f(x,y,z,...) is also a triangular dual of h(x,y,x,...). For example, sinx is the triangle dual of cosx; cos(x+y) is the triangle dual of -cos(x+y); sinx+cosy is the triangle dual of cosx+siny. Constructing the triangle duality h(x,y,z,...) of f(x,y,z,...), using the addition or subtraction, multiplication, division, complex number calculations of f and h, can solve many triangular problems. More concise. At the same time, constructing a dual equation for a trigonometric problem provides an important method for preparing a new trigonometric problem.