tanα＝3/根号3，π＜α＜2/3π，则sin2α的值是？
\uff081+tan\u03b1\uff09/\uff081-tan\u03b1\uff09=3+2\u6839\u53f72 \u5219sin2\u03b1=tan(\u03b1+\u03c0/4)=3+2\u6839\u53f72
sin2\u03b1=-cos(2\u03b1+\u03c0/2)==-cos2(\u03b1+\u03c0/4)=-[1-tan^2(\u03b1+\u03c0/4)]/[1+tan^2(\u03b1+\u03c0/4)]=(2/3)\u221a2
\u89e3
tana=\u221a3/3
\u03c0<a<3\u03c0/2
\u2234a=7\u03c0/6
\u2234sina=-1/2,cosa=-\u221a3/2
\u2234sin2a
=2sinacosa
=2\u00d7(-1/2)\u00d7(-\u221a3/2)
=\u221a3/2
∵tanα＝3/√3=√3，π＜α＜2/3π
∴α=4π/3
sin2α=sin(8π/3)=sin(2π+2π/3)=sin(2π/3)=√3/2
3/根号3 是三分之根号3
还是根号三分之三？
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