三角函数:设a为锐角,若cos(a+π/6)=4/5,则sin(2a+π/12)的值为多少?

问题描述:

三角函数:设a为锐角,若cos(a+π/6)=4/5,则sin(2a+π/12)的值为多少?

设α为锐角,若cos(α+
π6)=
35,则sin(2α+
π12)=
31
25031
250

3/5

a是锐角
π/2

sin(2a+π/12)=sin(2a+π/3 -π/4)
令a+π/6=x
于是化简成sin(2x-π/4)=sin2xcosπ/4-cos2xsinπ/4=2sinxcosxcosπ/4-(2cosxcosx-1)sinπ/4
带入已知条件cosx=4/5 sinx=3/5
得到待求式子=2*0.8*0.6*cosπ/4-7/25sinπ/4=17/25 *(1/2)^1/2