化简sin(x+60)+2sin(x-60)-( 根号3)cos(120-x)求详解

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化简sin(x+60)+2sin(x-60)-( 根号3)cos(120-x)求详解
化简sin(x+60)+2sin(x-60)-( 根号3)cos(120-x)
求详解

化简sin(x+60)+2sin(x-60)-( 根号3)cos(120-x)求详解
原式=SIN(X+60°)-(根号3)COS(120°-X)+2SIN(X-60°) =SIN(X+60°)+(根号3)COS(180°-120°+X)+2SIN(X-60°) =2[(1/2)SIN(X+60°)+(根号3/2)COS(X+60°)]+2SIN(X-60°) =2[SIN30°SIN(X+60°)+COS30°COS(X+60°)]+2SIN(X-60°) =2COS(30°-X-60°)+2SIN(X-60°) =2COS(-X-30°)+2SIN(X-60°) =2COS(X+30°)+2SIN(X-60°) =2SIN(90°-X-30°)+2SIN(X-60°) =2SIN(60°-X)-2SIN(60°-X) =0