、设a为锐角,若cos(a+pi/6)=4/5,则sin(2a+pi/12)的值为?

题目

、设a为锐角,若cos(a+pi/6)=4/5,则sin(2a+pi/12)的值为?
（问题同上）
求高手相助.深夜打扰真过意不去,还望海涵.

答案

a为锐角,cos(a+π/6)=4/5
所以,sin(a+π/6)=3/5
sin(2a+π/3)=2sin(a+π/6)cos(a+π/6)=2×(3/5)×(4/5)=24/25
cos(2a+π/3)=cos²(a+π/6)-sin²(a+π/6)=16/25-9/25=7/25
sin(2a+π/12)
＝sin[(2a+π/3)-π/4]
＝sin(2a+π/3)×cos(π/4)－cos(2a+π/3)×sin(π/4)
＝(24/25)×(√2/2)－(7/25)×(√2/2)
＝17√2/50