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Prove the following trigonometric identities: tan^2A/1+tan^2A+cot^2/1+cot^2A=1

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Prove the following trigonometric identities:

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

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

= \(\frac{sin^2A}{\frac{cos^2A}{\frac{1}{cos^2A}}}+\frac{cos^2A}{\frac{sin^2A}{\frac{1}{sin^2A}}}\) 

= sin2A + cos2A

=1

Hence Proved.

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