已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa
问题描述：
已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa
答
a∈(0,π/3)∴ a+π/6∈(π/6,π/2)∴ cos(a+π/6)>0∴ cos(a+π/6)=√[1-sin²(a+π/6)]=√(1-16/25)=3/5∴ cosa=cos[(a+π/6)-π/6]=cos(a+π/6)cos(π/6)+sin(a+π/6)sin(π/6)=(3/5)*(√3/2)+(4/5)*(1/2)=(3...