$\frac{\left(1+\tan ^{2} \mathrm{~A}\right) \cot \mathrm{A}}{\operatorname{cosec}^{2} \mathrm{~A}}$ is equal to

Expression:

$=\frac{\left(1+\tan ^{2} \mathrm{~A}\right) \cot \mathrm{A}}{\operatorname{cosec}^{2} \mathrm{~A}}$

$=\sec ^{2} \mathrm{~A} \cdot \cot \mathrm{A} \cdot \sin ^{2} \mathrm{~A}$

$(\sin A \cdot \operatorname{cosec} A=1)$

$=\frac{1}{\cos ^{2} \mathrm{~A}} \cdot \frac{\cos \mathrm{A}}{\sin \mathrm{A}} \cdot \sin ^{2} \mathrm{~A}$

$=\frac{\sin \mathrm{A}}{\cos \mathrm{A}}=\tan \mathrm{A}$