若A是锐角,sin(A-π/6)=1/3,则cosA的值等于多少? 要过程

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若A是锐角,sin(A-π/6)=1/3,则cosA的值等于多少? 要过程

cosA=cos(A-π/6+π/6)=cos(A-π/6)cosπ/6-sin(A-π/6)sinπ/6
0<A<π/2
-π/6<A-π/6<π/3
cos(A-π/6)>0
sin(A-π/6)=1/3
cos(A-π/6)=(2√2)/3
cosA=(2√2)/3*√3/2-(1/3)*(1/2)
=√6/3-(1/6)
=[(2√6)-1]/6