Question

急急急在线等！三角函数一题

Answer 1

这题要把角换成边：
2a^2=(2b+c)b+(2c+b)c
a^2=b^2+c^2+bc
由余弦定理
a^2=b^2+c^2-2bcosA
对比
2cosA=-1
A=2π/3

sinB+sinC = sinB + sin(π/3-B) = sinB + sin(π/3)cosB-cos(π/3)sinB = 1/2sinB + √3/2sinB = sinBcos(π/3)+cosBsin(π/3)= sin(B+π/3) =1
B+π/3=π/2
B=π/6
C=π/3-B=π/6
B=C
从而为等腰三角形。