本文给出用辅助函数法解题的若干例子。由此可以看出辅助函数法应用的一斑。例1 已知acosθ+bsinθ=c,acosφ+bsinφ=c((θ-φ)/2≠kπ,k为整数)。求证a/cos(θ+φ)/2=b/sin(θ+φ)/2=c/cos(θ-φ)/2 证明作辅助函数f=(x,y)=ax+by-c,则点P(cosθ,sinθ),Q(cosφ,sinφ)在直线f(x,y)=0上,此时直线方程为ax+by=c,由两点式可得 (y-sinθ)/(x-cosθ) =(sinθ-sinφ)/(cosθ-cosφ) ∴xcos[(θ+φ)/2]+ysin[(θ+φ)/2] =cos[(θ-φ)/2], This article gives some examples of problem solving using the auxiliary function method. From this we can see the application of the auxiliary function method. Example 1 It is known that acosθ+bsinθ=c, acosφ+bsinφ=c ((θ-φ)/2≠kπ, and k is an integer). Prove that a / cos (θ + φ) / 2 = b / sin (θ + φ) / 2 = c / cos (θ-φ) / 2 proved as an auxiliary function f = (x, y) = ax + by-c The point P(cosθ, sinθ) and Q(cosφ, sinφ) are on the straight line f(x,y)=0, and the linear equation is ax+by=c, which is obtained from two points (y-sinθ). /(x-cosθ) =(sinθ-sinφ)/(cosθ-cosφ) ∴xcos[(θ+φ)/2]+ysin[(θ+φ)/2] =cos[(θ-φ)/2 ],