【题目】-|||-lim _(xarrow infty )x|sin (1+dfrac (3)(x))-sin ln (1+dfrac (1)(x))|-|||-三角函数的和差化积公式和积化和差公式-|||-sin x+sin y=2sin dfrac (x+y)(2)cos dfrac (x)(2) . sin x-sin y=2cos dfrac (x+y)(2)sin dfrac (xy)(2)-|||-cos x+cos y=2cos dfrac (x+y)(2)cos dfrac (x-y)(2) .cos x-cos y=-2sin dfrac (x+y)(2)sin dfrac (x-y)(2)-|||-sin xcos y=dfrac (1)(2)[ sin (x+y)+sin (x-y)] cos xsin y=dfrac (1)(2)[ sin (x+y)-sin (x-y)] -|||-cos xcos y=dfrac (1)(2)[ cos (x+y)+cos (x-y)] sin xsin y=-dfrac (1)(2)[ cos (x+y)-cos (x-y)]