Question

17题怎么做？要过程

Answer 1

请采纳

追问

题目都不一样

Answer 2

ccosB=(2a-b)cosC
sinCcosB=2sinAcosC-sinBcosC
2sinAcosC=sinBcosC+sinCcosB
2sinAcosC=sin(B+C)

2sinAcosC=sinA
cosC=1/2
C=π/3
2) 2R=a/sinA=b/sinB=c/sinC=√3/√3/2=2
L=a+b+c=√3+2RsinA+2RsinB
=√3+2sinA+2sinB
=√3+2sinA+2sin(2π/3-A)
=√3+2sinA+√3cosA+sinA
=√3+3sinA+√3cosA
=√3+2√3(√3/2sinA+√1/2cosA)
=√3+2√3sin(A+π/6)
A在(0,2π/3)
A+π/6在(π/6,5π/6)
sin(A+π/6)在(π/6,5π/6)的值域为:(1/2,1]
L==√3+2√3sin(A+π/6)在(π/6,5π/6)的值域为:(2√3,3√3]
L最大值=3√3

追问

看不懂

追答

C=π/3
A+B=2π/3
B=2π/3-A
主要是把边转换成角
公式:2R=a/sinA=b/sinB=c/sinC
a=2RsinA ,b=2RsinB
L=a+b+c
=√3+2sinA+2sinB
=3+2sinA+2sin(2π/3-A)
==√3+2sinA+√3cosA+sinA
=√3+3sinA+√3cosA
=√3+2√3(√3/2sinA+√1/2cosA)
=√3+2√3sin(A+π/6)
A在(0,2π/3)
A+π/6在(π/6,5π/6)
sin(A+π/6)在(π/6,5π/6)的值域为:(1/2,1]
L==√3+2√3sin(A+π/6)在(π/6,5π/6)的值域为:(2√3,3√3]
L最大值=3√3