Question

sinB=sinC=sin2A,求A

Answer 1

sinB=sinC=sin2A
B，C∈(0，π/2)
B=C
A=π-(B+C)
∴sinC=sin2A
=sin(2π-4C)
C=2π-4C
∴C=2π/5
A=π/5

Answer 2

ABC是不是三角形的三个角？
如果是的话A+B+C=π
而且B=C
代入得A=π-2C
故：sinC=sin2A
sinC=sin2（π-2C)
sinC=-sin4C
sinC=4sinC^3×cosC-4sinC×cosC^3
1/4=sinC^2×cosC-cosC^3
1/4=cosC-2cosC^3
cosC=1/2
既C=π/3=A=B