0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x

0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x
0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x

0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x
tan(x+π/4)=1/7
则tanx
=tan[(x+π/4)-π/4]
=[tan(x+π/4)-tan(π/4)]/[1+tan(x+π/4)tan(π/4)]
=(1/7-1)/(1+1/7)
=-3/4
即 sinx/cosx=-3/4
与sin²x+cos²x=1联立
则 sinx=3/5,cosx=-4/5
∴ sinx+cosx=-1/5