解决一道高一数学题，求详细过程！

更新时间2022-04-10 21:32:18

已知sin(x+π/3)=1/3，则sin(5π/3-x)-cos(2x-π/3)的值为____-___
求详细过程，悬赏丰厚，各位数学大佬不要错过！

sin( 5π/3 - x ) - cos( 2x - π/3 )

= sin( 2π - π/3 - x ) - cos[ 2x - ( π - 2π/3 ) ]

= sin( -π/3 - x ) - cos[ π - 2( x + π/3 ) ]

= -sin( x + π/3 ) + cos[ 2( x + π/3 ) ]

= -sin( x + π/3 ) + 1 - 2[ sin( x + π/3 ) ]^2 代入 sin( x + π/3 ) = 1/3

= 1 - 1/3 - 2/9

= 4/9 。