在三角形ABC中b²+c²=a²+bc,(1)求角A(2)若sin²B/+sin²C/=1,判断形状搞错了,sin²B/+sin²C/=1应是sin²B/2+sin²C/2=1
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 23:36:19
![在三角形ABC中b²+c²=a²+bc,(1)求角A(2)若sin²B/+sin²C/=1,判断形状搞错了,sin²B/+sin²C/=1应是sin²B/2+sin²C/2=1](/uploads/image/z/10322981-53-1.jpg?t=%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%ADb%26%23178%3B%2Bc%26%23178%3B%3Da%26%23178%3B%2Bbc%2C%EF%BC%881%EF%BC%89%E6%B1%82%E8%A7%92A%EF%BC%882%EF%BC%89%E8%8B%A5sin%26%23178%3BB%2F%2Bsin%26%23178%3BC%2F%3D1%2C%E5%88%A4%E6%96%AD%E5%BD%A2%E7%8A%B6%E6%90%9E%E9%94%99%E4%BA%86%EF%BC%8Csin%26%23178%3BB%2F%2Bsin%26%23178%3BC%2F%3D1%E5%BA%94%E6%98%AFsin%26%23178%3BB%2F2%2Bsin%26%23178%3BC%2F2%3D1)
在三角形ABC中b²+c²=a²+bc,(1)求角A(2)若sin²B/+sin²C/=1,判断形状搞错了,sin²B/+sin²C/=1应是sin²B/2+sin²C/2=1
在三角形ABC中b²+c²=a²+bc,(1)求角A(2)若sin²B/+sin²C/=1,判断形状
搞错了,sin²B/+sin²C/=1应是sin²B/2+sin²C/2=1
在三角形ABC中b²+c²=a²+bc,(1)求角A(2)若sin²B/+sin²C/=1,判断形状搞错了,sin²B/+sin²C/=1应是sin²B/2+sin²C/2=1
b²+c²=a²+bc,
bc=b²+c²-a²
cosA=(b²+c²-a²)/2bc=bc/2bc=1/2
A=60度
sin²B+sin²C=1,
1/2(1-cos2B)+1/2(1-cos2C)=1
cos2B+cos2C=0
cos(B+C)cos(B-C)=0
cosAcos(B-C)=0
cos60cos(B-C)=0
cos(B-C)=0
B=C,A=60度
三角形ABC是等边三角形