证明sin(a+b)sin(a-b)=sin²a-sin² b,并用该式计算sin²20°+sin80°sin40°
问题描述：
证明sin(a+b)sin(a-b)=sin²a-sin² b,并用该式计算sin²20°+sin80°sin40°
答
sin(a+b)sin(a-b)=(sinacosb+sinbcosa)(sinacosb-sinbcosa) =(sinacosb)^2+sinasinbcosacosb-sinasinbcosacosb-(sinbcosa)^2 =(sinacosb)^2-(1-sin^2a)(1-cos^2b) =(sinacosb)^2-[1-sin^2a-cos^2b+(sinacosb)^2] =-1...