若α是锐角,且满足sin(α-π/6)=1/3,则cos阿尔法的值为多少 thanks!

题目

若α是锐角,且满足sin(α-π/6)=1/3,则cos阿尔法的值为多少 thanks!

答案

sin(α-π/6)=1/3,cos(α-π/6)=2√2/3;
cos(α)=cos(α-π/6+π/6)=cos(α-π/6)cosπ/6-sin(α-π/6)sinπ/6=(根号6)/3-1/6