Simplify the fraction $\frac{\cot\left(x\right)\left(\cos\left(x\right)+\tan\left(x\right)\sin\left(x\right)\right)}{\cot\left(x\right)\left(\cos\left(x\right)+\sin\left(x\right)\tan\left(x\right)\right)}$ by $\cot\left(x\right)\left(\cos\left(x\right)+\tan\left(x\right)\sin\left(x\right)\right)$
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