Question

$\large{\underline{\underline{\bf\maltese\; Prove\; that\; LHS=RHS}}}$

$\Large{\displaystyle{\Bigg[\Bigg(\dfrac{1+\tan^2\theta}{1+\cot^2\theta}\Bigg)-\Bigg(\dfrac{1-\tan\theta}{1-\cot\theta}\Bigg)^2\;\Bigg]=\tan^2\theta}}$

Related identities:

$\begin{gathered}\bullet\;1+\tan^2\theta=\sec^2\theta\\\\\bullet\;1+\cot^2\theta=cosec^2\theta\\\\\bullet\;\cos^2\theta+\sin^2\theta=1\end{gathered}$

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Answer 1

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Answer 2

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