您的位置: 首页 > 作业答案 > 数学 > a属于(π/2,π),1/sina+1/cosa=2根号2,则sin(2a+π/3)=______ a属于(π/2,π),1/sina+1/cosa=2根号2,则sin(2a+π/3)=______ 分类: 作业答案 • 2021-12-28 14:06:12 问题描述: a属于(π/2,π),1/sina+1/cosa=2根号2,则sin(2a+π/3)=______ 答 (sina+cosa)/sinacosa=2√2sina+cosa=2√2sinacosa平方sin²a+cos²a+2sinacosa=8(sinacosa)²1+sin2a=8(1/2*sin2x)²=2sin²2a(2sin2a+1)(sin2a-1)=0π/2πsin2a所以sin2a=-1/2所以2a=7π/6或11π/61/sina+1/cosa>01/sina>-1/cosasina>0,cosa所以sinasina+cosa√2sin(a+π/4)所以2a=11π/6舍去2a=7π/62a+π/3=3π/2所以sin(2a+π/3)=-1