a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)
问题描述：
a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)
答
sin(2a+π/12)=cos[2(a+π/6)-π/4]=√2/2(cos[2(a+π/6)]+sin[2(a+π/6)])
因为cos(a+π/6)=4/5,所以sin(a+π/6)=3/5
cos[2(a+π/6)]=2[cos(a+π/6)]²-1=7/25,sin[2(a+π/6)]=cos(a+π/6)*sin(a+π/6)=24/25。
所以结果为√2/2*（31/25)=31√2/50.
答
a是锐角
π/2