tanx=-1/2,sinx平方+3sinx*cosx-1=?

题目

tanx=-1/2,sinx平方+3sinx*cosx-1=?

答案

sin²x+3sinxcosx-1
=(3sinxcosx-cos²x)/(sin²x+cos²x)
=(3tanx-1)/(tan²x+1)
=(3×(-1/2)-1)/[(-1/2)²+1]
=(-5/2)/(5/4)
=-2