Prove the following identities: `(cos^2theta)/(1-tantheta)+(sin^3theta)/(sintheta-costheta)=1+sinthetacostheta`

Explanation

To prove the identity

\[ \frac{\cos^2 \theta}{1 - \tan \theta} + \frac{\sin^3 \theta}{\sin \theta - \cos \theta} = 1 + \sin \theta \cos \theta, \]

we will start from the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

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