证明sin(2a+p)/sina-2cos(a+p)=sinp/sina

分类: 作业答案 • 2021-12-19 15:55:27

问题描述：

答

证：
sin(2a+p)/sina-2cos(a+p)
=[sina cos(a+p)+cosa sin(a+p)]/sina-2cos(a+p)
=[cosa sin(a+p)-sina cos(a+p)]/sina
=sin(a+p-a)/sina
=sinp/sina
证毕

答

sin(2a+p)/sina-2cos(a+p)
= (sin2acosp+cos2asinp) / sina - 2cosacosp+2sinasinp
= 2cosacosp + (1-2sina^2)sinp/sina - 2cosacosp+2sinasinp
= sinp/sina