4.    Choose the correct option. Justify your choice.

     (iv) \frac{1+\tan ^{2}A}{1+\cot ^{2}A}=

     (A) \sec ^{2}A   (B) -1  (C) \cot ^{2}A    (D) \tan ^{2}A

Answers (1)
M manish

The correct option is (D)

\frac{1+\tan ^{2}A}{1+\cot ^{2}A}..........................eq (i)

The above equation can be written as;

We know that \cot A = \frac{1}{\tan A}

therefore,

\\\Rightarrow \frac{1+\tan ^{2}A}{1+\frac{1}{\tan ^{2}}A}\\ \Rightarrow \tan^2A\times(\frac{1+\tan^2 A}{1+\tan^2A})\\ \Rightarrow \tan^2A

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