Question

[sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2013,tan(x+5π/4)=

Answer 1

[sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2013
根据诱导公式，化简
(cosx+sinx)/(cosx-sinx)=2013
左边分子分母同时除以cosx:
(1+tanx)/(1-tanx)=2013
∵tan5π/4=tan(π+π/4)=1
∴(tan5π/4+tanx)/(1-tan5π/4tanx)=2013
根据两角和正切公式
tan(x+5π/4)=(tan5π/4+tanx)/(1-tan5π/4tanx)
∴tan(x+5π/4)=2013

Answer 2

一般思路是。。先把原式化简，再上下同除以cosx，最后求tanx