若cos（a+π/6）等于4/5，则sin（2a+π/12）的值为？ 大家帮忙

Question

如题所述

Answer 1

是不是少了一个条件： a为锐角？

如果是，解答如下：

a是锐角π/2<a+π/6<2π/3cos(a+π/6)=4/5,sin(a+π/6)=3/5sin(2a+π/3)=2sin(a+π/6)cos(a+π/6)=2*(4/5)*(3/5)=24/25cos(2a+π/3)=2cos�0�5(a+π/6)-1=2*(4/5)�0�5-1=7/25sin(2a+π/12)=sin[(2a+π/3)-π/4]=sin(2a+π/3)cos(π/4)-cos(2a+π/3)cos(π/4)=(24/25)*(√2/2)-(7/25)*(√2/2)=17√2/50