Question

已知π/4<θ<π,tan(θ+π/4)=1/7,那么sinθ+cosθ=

Answer 1

（tanθ+tanπ/4)/(1-tanπ/4 *tanθ)=1/7
tanθ=-3/4
因为π/4<θ<π
so sinθ=3/5 cosθ=-4/5
sinθ+cosθ=-1/5

Answer 2

tan(a+π/4)=(tana+1)/(tana-1)=1/7
解得tana=4/3 因为π/4<a<π
所以π/4<a<π/2 正余弦都为正
sina=4/5 cosa=3/5
sina+cosa=7/5