Question

$\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}=?$
(a) –1
(b) sec²A
(c) tan²A
(d) cot²A

Answer 1

$$\begin{gathered} \frac{1+{\tan }^{2}A}{1+{\cot }^{2}A} \\ =\frac{{\sec }^{2}A}{{\mathrm{cosec}}^{2}A} \\ =\frac{{\sin }^{2}A}{{\cos }^{2}A}\left(\sec \theta =\frac{1}{\cos \theta }\mathrm{and}\mathrm{cosec}\theta =\frac{1}{\sin \theta }\right) \\ ={\tan }^{2}A \end{gathered}$$

Hence, the correct answer is option (c).