已知cos(α+π/4）=4/5,则tanα=
问题描述：
已知cos(α+π/4）=4/5,则tanα=
答
以为cos(α+π/4）=4/5，所以sinα(α+π/4）=正负3/5，所以tan(α+π/4）=正负3/4，因为tan(α+π/4）=tanα+tanπ/4/1-tanα*tanπ/4，所以1+tanα=正负3/4*1-tanα，之后解方程就行了，求给分......
答
cos(α+π/4）=4/5
则sin(α+π/4）=3/5 或 sin(α+π/4）=-3/5
tan(α+π/4）=3/4 或 tan(α+π/4）=-3/4
(tanα+tanπ/4)/(1-tanαtanπ/4)=3/4
(tanα+1)/(1-tanα)=3/4
4tanα+4=3-3tanα
tanα=-1/7
或
(tanα+tanπ/4)/(1-tanαtanπ/4)=-3/4
(tanα+1)/(1-tanα)=-3/4
4tanα+4=3tanα-3
tanα=-7