问题 填空题
化简sin(x+60°)+2sin(x-60°)-
3
cos(120°-x)的结果是 ______.
答案

原式=sin(x+60°)-

3
cos[180°-(x+60°)]+2sin(x-60°)

=sin(x+60°)+

3
cos(x+60°)+2sin(x-60°)

=2sin(x+60°+60°)+2sin(x-60°)

=2sin(x-60°+180°)+2sin(x-60°)

=-2sin(x-60°)+2sin(x-60°)

=0.

故答案为0

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