[tex]\bf \lim\limits_{x\to 0}\ cot(2x)sin(6x)\implies \lim\limits_{x\to 0}\ \cfrac{cos(2x)}{sin(2x)}sin(6x)\\\\
-----------------------------\\\\
\underline{LH}\qquad \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
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\lim\limits_{x\to 0}\ \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
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\lim\limits_{x\to 0}\ \cfrac{-0\cdot 0+1\cdot 6\cdot 1}{2\cdot 1}\implies \cfrac{6}{2}\implies 3[/tex]
