已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa

已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa
已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa

已知sin(a+π/6)=4/5 a∈(0,π/3) 求cosa
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√3+4)/10