cos(α+β)=sin(α-β),tanα=?

题目

cos(α+β)=sin(α-β),tanα=?

答案

cos(α+β)=sin(α-β)
cosacosb-sinasinb=sinacosb-cosasinb
cosacosb+cosasinb=sinacosb+sinasinb
cosa(cosb+sinb)=sina(cosb+sinb)
cosa=sina
tanα=1