在△ABC中,证明:cos2A/a²-cos2B/b²=1/a²-1/b²感激不尽!
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 19:54:07
![在△ABC中,证明:cos2A/a²-cos2B/b²=1/a²-1/b²感激不尽!](/uploads/image/z/6952523-59-3.jpg?t=%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E8%AF%81%E6%98%8E%3Acos2A%2Fa%26%23178%3B-cos2B%2Fb%26%23178%3B%3D1%2Fa%26%23178%3B-1%2Fb%26%23178%3B%E6%84%9F%E6%BF%80%E4%B8%8D%E5%B0%BD%21)
在△ABC中,证明:cos2A/a²-cos2B/b²=1/a²-1/b²感激不尽!
在△ABC中,证明:cos2A/a²-cos2B/b²=1/a²-1/b²
感激不尽!
在△ABC中,证明:cos2A/a²-cos2B/b²=1/a²-1/b²感激不尽!
根据正弦定理得:
sinA/a=sinB/b
cos2A/a^2-cos2B/b^2
=[1-(sinA)^2]/a^2-[1-(sinB)^2]/b^2
=1/a^2-1/b^2-[(sinA)^2/a^2-(sinB)^2/b^2]
=1/a^2-1/b^2
所以cos2A/a^2-cos2B/b^2=1/a^2-1/b^2