作业帮证明sin(a+b)sin(a-b)=sin²a-sin² b,并用该式计算sin²20°
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/16 00:49:32
证明sin(a+b)sin(a-b)=sin²a-sin² b,并用该式计算sin²20°+sin80°sin40°
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+sin^2a+(1-sin^2b)
=sin^2 a-sin^2 b
sin²20°+sin80°sin40°
=sin²20°+sin(60°+20°)sin(60°-20°)
=sin²20°+sin²60°-sin²20°
=sin²60°
=(√3/2)²
=3/4
=(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+sin^2a+(1-sin^2b)
=sin^2 a-sin^2 b
sin²20°+sin80°sin40°
=sin²20°+sin(60°+20°)sin(60°-20°)
=sin²20°+sin²60°-sin²20°
=sin²60°
=(√3/2)²
=3/4
证明sin(a+b)sin(a-b)=sin²a-sin² b,并用该式计算sin²20°
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b, 并利用该式计算sin^2 20度=sin 80度
【证明】Sin A+sin B=2Sin 22
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
sin²A+sin²B=cos²C
求证：sin²A+sin²B-sin²A·sin²B+cos²A·co
sin²A=sin²B+sin²C,求三角形ABC形状
证明sin(a+b)=sinacosb+cosasinb
证明：三角形ABC中,若sin²A+sin²B+sin²C＜2,三角形ABC为钝角三角形
在△ABC中,若sin(A+B)sin(A-B)=sin²C,则此三角形形状是
1:sin(a-b)=sin(-b+a)
在直角三角形ABC中 角C =90°证明sin²A+sin²B=1