0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x
问题描述：
0小于x小于派,tan（x+π/4）=1/7,求sin x+cos x
答
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...