Question

已知A,B,C是三角形ABC三内角,向量M=(-1,根号3).向量N=(COSA,SINA),且向量M点乘向量N=1

Answer 1

M*N=-cosA+√3sinA=2sin(A-π/3)=1

sin(A-π/3)=1/2

A=π/2

(1+sin2B)/[(cosB)^2-(sinB)^2]

=(sinB+cosB)^2/(sinB+cosB)(cosB-sinB)

=(sinB+cosB)/(cosB-sinB)（分子分母同除cosB)

=(tanB+1)/(1-tanB)

=-3

tanB=2