解决一道高一数学题,求详细过程!
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 。
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