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

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

已知sin(π/6+a)=4/5,a∈(π/3,5π/6),求cosa的值.
a∈(π/3,5π/6),则π/6+a∈(π/2,π)
sin(π/6+a)=4/5,则cos(π/6+a)=-3/5
cosa=cos[(π/6+a)-π/6]
=cos(π/6+a)cos(π/6)+sin(π/6+a)sin(π/6)
=(-3/5)(√3/2)+(4/5)(1/2)
=(4-3√3)/10
祝你开心!希望能帮到你,如果不懂,请追问,祝学习进步!O(∩_∩)O

∵a∈(π/3,5π/6)
∴π/6+a∈(π/2,π) cos(π/6+a)=-3/5
sin(π/6+a-a)=sin(π/6+a)cosa-cos(π/6+a)sina=(4/5)cosa-(-3/5)sina=sinπ/6=1/2
cos(π/6+a-a)=cos(π/6+a)cosa+sin(π/6+a)sina=(-3/5)cosa+(4/5)sina=cosπ/6=√3/2
sina=(4√3+3)/10
cosa=(4-3√3)/10