3sinθtanθ=8,（0＜θ＜π）,则cos（θ-π/4）=
问题描述：
3sinθtanθ=8,（0＜θ＜π）,则cos（θ-π/4）=
答
∵0＜θ＜π∴sinθ>0∵3sinθtanθ=8==>3(sinθ)^2/cosθ=8==>(sinθ)^2=8cosθ/3==>(cosθ)^2+8cosθ/3=1 (∵(sinθ)^2+(cosθ)^2=1)==>3(cosθ)^2+8cosθ-3=0==>(3cosθ-1)(cosθ+3)=0==>3cosθ-1=0 (∵cosθ+3>0...