帮忙~~~~~啊~~已知αβ均为锐角cos(α+β)=sin(α-β)则tanα=

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帮忙~~~~~啊~~已知αβ均为锐角cos(α+β)=sin(α-β)则tanα=
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帮忙~~~~~啊~~已知αβ均为锐角cos(α+β)=sin(α-β)则tanα=
帮忙~~~~~啊~~
已知αβ均为锐角cos(α+β)=sin(α-β)则tanα=

帮忙~~~~~啊~~已知αβ均为锐角cos(α+β)=sin(α-β)则tanα=
cos(α+β)=sin(α-β)
cosacosβ-sinasinβ=sinacosβ-sinβcosa
cosa(cosβ+sinβ)=sina(cos β+sin β)
cosa=sina
所以tana=1

α=β=π/4,所以tanα=1

展开得COSACOSB-SINASINB=SINACOSB-COSASINB
移项整理有COSA(SINB+COSB)=SINA(SINB+COSB)
即SINA=COSA
TANA=1

两边平方并整理得a=45
tan a=1
谢谢采纳