Question

已知a属于(0,派)且cos(a-派/6)=3/5.求cosa.

Answer 1

a属于(0,派)且cos(a-派/6)=3/5
所以
sin(a-派/6)=4/5
从而
cosa=cos（a-π/6＋π/6）
=cos（a-π/6）cosπ/6-sin（a-π/6）sinπ/6
=3/5×√3/2-4/5×1/2
=（3√3-4）/10

Answer 2

∵1/2<3/5<√2/2
∴π/4<a-π/6<π/3或-π/3<a-π/6<-π/4
即5π/12<a<π/2或-π/6<a<-π/12
又∵a属于(0，π)
∴5π/12<a<π/2
即π/4<a-π/6<π/3
∴sin(a-π/6)=√[1-cos²(a-π/6)]=4/5
cosa=cos[(a-π/6)+π/6]
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
=3/5*(√3/2)-4/5*(1/2)
=(3√3-4)/10

Answer 3

0<a<Pai.

-Pai/6<a-Pai/6<5Pai/6
故有sin(a-Pai/6)=(+/-)4/5
cosa=cos(a-Pai/6+Pai/6)
=cos(a-Pai/6)cosPai/6-sin(a-Pai/6)sinPai/6
=3/5*根号3/2-(+/-)4/5*1/2
=(3根号3(-/+)4)/10