Question

在△ABC中,内角A、B、C,若sinA=cosB,则C=?

Answer 1

sinA=cosB 或 sin(180-A)=cosB=sin(90-B)

sinB=cosA 180-A=90-B

cosC=-cos(A+B)=sinAsinB-cosAcosB=0 A=90+B

C=90,cosA=-sinB

cosC=-cos(A+B)=sinAsinB-cosAcosB

=-2sinAcosA=-sin2A

C=180-A-B=90-2B