题目

已知6sin^2(A)+sinAcosA-2cos^2(A)=0,派/2=

提问时间：2021-01-02

答案

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6(sina)^2+sinacosa-2(cosa)^2=0
(2sina-cosa)(3sina+2cosa)=0
2sina-cosa=0,sina/cosa=1/2
3sina+2cosa=0.sina/cosa=-2/3
π/2<=a<=π
所以sina>0,cosa<0
sina/cosa<0
所以sina/cosa=-2/3
sina=-2cosa/3
(sina)^2+(cosa)^2=1
4(cosa)^2/9+(cosa)^2=1
(cosa)^2=9/13
cosa=-3/√13
sina=2/√13
sin2a=2sinacosa=-12/13
cos2a=2(cosa)^2-1=5/13
sin(2a+π/3)
=sin2acosπ/3+cos2asinπ/3
=(-12/13)*(1/2)+(5/13)*√3/2
=(5√3-12)/26