求证sin(A+B)/cos(A-B)=(tanA+tanB)/(1+tanAtanB)如题,sin(A+B)/cos(A-B)=_数学解答

求证sin(A+B)/cos(A-B)=(tanA+tanB)/(1+tanAtanB)
如题,
sin(A+B)/cos(A-B)=(tanA+tanB)/(1+tanAtanB)

人气：494 ℃　时间：2020-03-30 06:07:09

解答

sin(A+B)/cos(A-B)
=(sinAcosB+cosAsinB)/(cosAcosB+sinAsinB)
=[(sinAcosB+cosAsinB)/cosAcosB]/[(cosAcosB+sinAsinB)/cosAcosB]
=(tanA+tanB)/(1+tanAtanB)