题目

化简：sin(x+60°)+2sin(x-60°)-cos(120°-x). 答案：解:原式=sin(x+60°)-cos［180°-(60°+x)］+2sin(x-60°)=sin(x+60°)+cos(60°+x)+2sin(x-60°)=2［sin(x+60°)+cos(60°+x)］+2sin(x-60°)=2［cos60°sin(x+60°)+sin60°cos(60°+x)］+2sin(x-60°)=2sin(x+120°)+2sin(x-60°)=2sin(180°-60°+x)+2sin(x-60°)=-2sin(x-60°)+2sin(x-60°)=0.点评：本题运用“异角化同角”思路.

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