Prove each of the following identities :
` (tan theta)/((1-cot theta)) + (cot theta)/((1- tan theta)) = (1+ sec theta "cosec" theta) `

Explanation

To prove the identity

\[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \csc \theta, \]

we will start by rewriting the trigonometric functions in terms of sine and cosine.

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