tanx=m,则{sin(x+3π）+cos(π+x)}/{sin(-x)-cos(π+x）}=?

Question

tanx=m,则{sin(x+3π）+cos(π+x)}/{sin(-x)-cos(π+x）}=?

Answer 1

原式=[sin(2π+x+π)+cos(π+x)]/[-sinx-cos(π+x)]
=[sin(π+x)+cos(π+x)]/[-sinx-cos(π+x)]
=(-sinx-cosx)/(-sinx+cosx) (应用诱导公式)
=(sinx+cosx)/(sinx-cosx)
=(sinx/cosx+1)/(sinx/cosx-1)
=(tanx+1)/(tanx-1)
=(m+1)/(m-1)