已知sin(π/2-x)+sin(π-x)/cos(-x)+sin(2π-x)=2009,则tan(x+5π/4)等于?

问题描述:

已知sin(π/2-x)+sin(π-x)/cos(-x)+sin(2π-x)=2009,则tan(x+5π/4)等于?
已知sin(π/2-x)+sin(π-x)/cos(-x)+sin(2π-x)=2009,则tan(x+5π/4)等于() A.-2009 B.-1/2009 C.1/2009 D.2009

【参考答案】D[sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2009根据诱导公式,化简(cosx+sinx)/(cosx-sinx)=2009左边分子分母同时除以cosx:(1+tanx)/(1-tanx)=2009∵tan5π/4=tan(π+π/4)=1∴(tan5π/4+tanx)/(1-...