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Evaluate:
$\frac{1+tan^{2} A}{1+cot^{2} A}$
Solution:
Evaluate $\frac{1+tan^{2} A}{1+cot^{2} A}$
$ \begin{array}{l}
\frac{1+tan^{2} A}{1+cot^{2} A}\
\
=\ \frac{sec^{2} A}{cosec^{2} A}\
\
=\frac{\frac{1}{cos^{2} A}}{\frac{1}{sin^{2} A}}\
\
=\frac{sin^{2} A}{cos^{2} A}\
\
=tan^{2} A
\end{array}$
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