lim(sin3x/sinx)极限,x趋向π/2

原式=(sin3x*cosx-cos3x*sinx)/(sinx*cosx)
= 2sin(3x-x)/sin2x=2

sin3x=sin(2x+x)=sin2xcosx+cos2xsinx
=2sinxcosxcosx+(2cosx*cosx-1)sinx
所以,sin3x/sinx=2cosxcosx+2cosx*cosx-1
=4cosxcosx-1
所以4cosxcosx-1=13/5
cos2x=2cosxcosx-1=4/5
sin2x=3/5,或sin2x=-3/5
所以tan2x=3/4或tan2x=-3/4
看懂了吗?
不懂再问啊

sin3x=sin(2x+x)=sin2xcosx+cos2xsinx
=2sinxcosxcosx+[(cosx)^2-(sinx)^2]sinx
=3sinx(cosx)^2-(sinx)^3
=3sinx[1-(sinx)^2]-(sinx)^3
=sinx[3-4(sinx)^2]
=sinx[3-2(1-cos2x)]
=sinx(1+2cos2x)
∵sinx不等于0,∴sin3x/sinx=1+2cos2x=13/5
所以cos2x=4/5,∵x是第IV象限的角,2x是第III或第IV象限的角,所以tan2x=-3/4