Let us simplify each Expression Separately :
✿ [tex]\mathsf{(\frac{cot\theta.cos\theta}{sin\theta}).tan\theta}[/tex]
[tex]\mathsf{\implies (\frac{cot\theta.tan\theta.cos\theta}{sin\theta})}[/tex]
[tex]\mathsf{We\;know\;that : tan\theta.cot\theta = 1}[/tex]
[tex]\mathsf{\implies (\frac{cos\theta}{sin\theta})}[/tex]
[tex]\mathsf{We\;know\;that : cot\theta = \frac{cos\theta}{sin\theta} }[/tex]
[tex]\mathsf{\implies (\frac{cot\theta.cos\theta}{sin\theta}).tan\theta = cot\theta }[/tex]
✿ [tex]\mathsf{(\frac{sin\theta}{cos\theta.tan\theta})}[/tex]
[tex]\implies \mathsf{(\frac{\frac{sin\theta}{cos\theta}}{tan\theta})}[/tex]
[tex]\mathsf{We\;know\;that : tan\theta = \frac{sin\theta}{cos\theta} }[/tex]
[tex]\implies \mathsf{(\frac{tan\theta}{tan\theta})}[/tex]
[tex]\implies \mathsf{1}[/tex]
[tex]\mathsf{\implies (\frac{sin\theta}{cos\theta.tan\theta}) = 1}[/tex]
[tex]\mathsf{The\;Simplest\;form\;of\;the\;Given\;Expression\;is : cot\theta}[/tex]
