谁帮我解数学题？正弦定理中的！

来源：百度知道 编辑：UC知道 时间：2024/06/28 14:37:56
[（sin²B-sin²C）/sin²A]*sin2A为什么=sin2C-sin2B?
特急啊！我想了好多天都想不出来！请大家帮帮忙！

sin2C-sin2B
＝sin[(C+B)+(C-B)]-sin[(C+B)-(C-B)]
=2cos(C+B)sin(C-B)

{[(sinB)^2-(sinC)^2]/(sinA)^2}*sin2A
={[(sinB)^2-(sinC)^2]/(sinA)^2}*2sinAcosA
=[(sinB)^2-(sinC)^2]2cotA

要证
[(sinB)^2-(sinC)^2]cotA＝cos(C+B)sin(C-B)
要证
[(sinC)^2-(sinB)^2]cot(B+C)＝cos(C+B)sin(C-B)
要证
[(sinC)^2-(sinB)^2]cos(B+C)＝cos(C+B)sin(C-B)sin(B+C)
要证
2(sinC)^2-2(sinB)^2=2sin(C-B)sin(B+C)
要证
-1+2(sinC)^2+1-2(sinB)^2=2sin(C-B)sin(B+C)
要证
cos(2B)-cos(2C)=2sin(C-B)sin(B+C)
要证
cos2B-cos2C
＝-cos[(C+B)+(C-B)]+cos[(C+B)-(C-B)]
=2sin(C-B)sin(B+C)

证毕