a屬於（π/2,π）,1/sina 1/cosa=2根號2,則sin(2a π/3)=______網友廻答：
- (sina cosa)/sinacosa=2√2
sina cosa=2√2sinacosa
平方
sin²a cos²a 2sinacosa=8(sinacosa)²
1 sin2a=8(1/2*sin2x)²=2sin²2a
(2sin2a 1)(sin2a-1)=0
π/2πsin2a所以sin2a=-1/2
所以2a=7π/6或11π/6
1/sina 1/cosa>0
1/sina>-1/cosa
sina>0,cosa所以sinasina cosa√2sin(a π/4)所以2a=11π/6捨去
2a=7π/6
2a π/3=3π/2
所以sin(2a π/3)=-1
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