cos^2A - cos^2B + sin^2C=2cosA *sinB *sinC证明_数学解答

cos^2A - cos^2B + sin^2C=2cosA *sinB *sinC证明

人气：478 ℃　时间：2020-02-03 08:40:52

解答

左边=sin(A+B)sin(B-A)+sin²C
=sin(180-C)sin(B-A)+sin²C
=sinCsin(B-A)+sin²C
=sinC[sin(B-A)+sinC]
=sinC[sin(B-A)+sin(B+A)]
=sinC(sinBcosA-cosBsinA+sinBcosA+cosBsinA)
=sinC*2sinBcosA=右边
命题得证