Sin75°/Cos75°+Cos75°/Sin15°=?
问题描述：
Sin75°/Cos75°+Cos75°/Sin15°=?
答
原式=Sin75°/Cos75°+Cos75°/Sin15°
=Sin75°/Cos75°+Cos75°/Cos75°
=tan75°+1
=tan(30°+45°)+1
=（tan30°+tan45°）/(1-tan30°*tan45°) +1
=3+√3
注：sinx=cos(90-x ) tan(x+y)=(tanx+tany)/(1-tanx*tany)
答
tan75=(tan30+tan45)/(1-tan30*tan45)=2+√3
sin75/cos75+cos75/sin75=tan75+1/tan75=2+√3+1/(2+√3)=4
答
Sin75°/Cos75°+Cos75°/Sin15°
=Sin75°/Cos75°+Cos75°/Cos75°
=tan75°+1
=tan(30°+45°)+1
=（tan30°+tan45°）/(1-tan30°*tan45°) +1
=3+√3