若角α为锐角,且sin(a-π/6)=1/3,则cosα=?

若角α为锐角,且sin(a-π/6)=1/3,则cosα=?
若角α为锐角,且sin(a-π/6)=1/3,则cosα=?

若角α为锐角,且sin(a-π/6)=1/3,则cosα=?
sin(a-π/6)=1/3
cos(a-π/6)=√[1-sin^2(a-π/6)]=√(1-1/9)=2√2/3
sinacosπ/6-cosasinπ/6/2sina-1/2cosa=1/3
cosα=(a-π/6+π/6)
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
=(2√2/3)*(√3/2)-(1/3)*(1/2)
=(2√6-1)/6