已知0

题目

已知0<α<3π/4,cos(α+π/4)=3/5,则tana

答案

0<α<3π/4
∴π/4<α+π/4<π
cos(α+π/4)=3/5＞0
∴π/4<α+π/4<π/2
cos(α+π/4)=3/5
sin(α+π/4)=√{ 1-[cosα+π/4)]^2} = 4/5
tan(α+π/4) = sin(α+π/4)/cos(α+π/4) = 4/5 /(3/5) = 4/3
(tanα+tanπ/4)/(1-tanαtanπ/4) = 4/3
(tanα+1)/(1-tanα) = 4/3
3(tanα+1) = 4(1-tanα)
3tanα+3 = 4-4tanα
7tanα = 1
tanα = 1/7