若x是锐角,且满足sin(x-pai/6)=1/3,则cosx等于多少

题目

若x是锐角,且满足sin(x-pai/6)=1/3,则cosx等于多少

答案

解∵sin(x-π/6)=1/3,x是锐角
∴cos(x-π/6)=2√2/3
cosx=cos[(x-π/6)+π/6]=cos(x-π/6)cosπ/6-sin(x-π/6)sinπ/6
=(2√2/3)*(√3/2)-(1/3)*(1/2)
=(2√6-1)/6