求证:sin(A+B)sin(A-B)=sinAsinA-sinBsinB

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/19 06:15:41
求证:sin(A+B)sin(A-B)=sinAsinA-sinBsinB
x){{fgi8j;ii]'M[ u$铤^Άt^h먓d > uj`h+I$&'iD 'I. ­Ȍ33rBImYT&DMD (ul2Hw6<ٽĽ/xo:0 <;hۀ9Ov>]G syQ\$

求证:sin(A+B)sin(A-B)=sinAsinA-sinBsinB
求证:sin(A+B)sin(A-B)=sinAsinA-sinBsinB

求证:sin(A+B)sin(A-B)=sinAsinA-sinBsinB
令a=A,b=B

sin(A+B)sin(A-B)-(sinAsinA-sinBsinB)
=(sinacosb+cosasinb)(sinacosb-cosasinb)-(sinAsinA-sinBsinB)
=sin^2acos^2b-cos^2asin^2b-sin^2a+sin^2b
=sin^2a(cos^2b-1)-sin^2b(cos^2a-1)
=(cos^2a-1)sin^2b-sin^2b(cos^2a-1)
=0
所以命题得证
所以sin(A+B)sin(A-B)=sinAsinA-sinBsinB

不对的“公式”