Question

已知A B C是三角形ABC的三个内角,向量M=（-1,根号3）,向量N=（cosA,sinA),且向量M*向量N=1

Answer 1

m·n=(-1,√3)·(cosA,sinA)

=√3sinA-cosA

=2sin(A-π/6)=1

即：sin(A-π/6)=1/2

A是内角,故：A∈(0,π)

即：A-π/6∈(-π/6,5π/6)

故：A-π/6=π/6

即：A=π/3

(1+sin(2B))/(cosB^2-sinB^2)

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

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

=(tanB+1)/(1-tanB)=-3

即：tanB+1=-3+3tanB

即：tanB=2