Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(iii) `(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+sectheta cosectheta`

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 simplifying the left-hand side (LHS) and show that it equals the right-hand side (RHS).

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