已知sin30cosa-cos30sina=1/4，求sin(30+2a)的值？

来源：百度知道 编辑：UC知道 时间：2024/09/24 12:00:09
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sin30cosa-cos30sina
=sin(30-a)=1/4
cos(60-2a)=cos[2(30-a)]=1-2sin²(30-a)]=1-2*(1/4)²=7/8
sin(30+2a)=cos[90-(30+2a)]=cos(60-2a)=7/8

sin30cosa-cos30sina = sin(30-a) = 1/4

cos(30-a) = 根号(1-(1/4)^2) = 根号15 / 4

cos(60-2a) = 1 - 2*sin(30-a)^2 = 7/8

sin(30+2a) = cos(90-30-2a) = cos(60-2a) = 7/8

sin30cosa-cos30sina = sin(30-a) = 1/4
cos(30-a) = √(1-(1/4)^2) = √15 / 4
cos(60-2a) = 1 - 2*sin(30-a)^2 = 7/8
sin(30+2a) = cos(90-30-2a) = cos(60-2a) = 7/8