Question

1+ tan² A/1+ cot² A= tan² A

Answer 1

hope you get that................

Answer 2

$\frac{1 + {tan}^{2} A}{1 + {cot}^{2}A} = {tan}^{2} A$

From trigonometric identity

1+ tan² A = sec²A
1+ cot² A = cosec²A

$\frac{ {sec}^{2}A}{ {cosec}^{2}A} = {tan}^{2} A \\ \\ = > \frac{ \frac{1}{cos ^{2} A} }{ \frac{1}{sin ^{2}A} } = {tan}^{2} A \\ \\ = > \frac{ {sin}^{2}A}{cos ^{2} A} = {tan}^{2} A \\ \\ = > {tan}^{2} A = {tan}^{2} A$

LHS = RHS

Hence proved