Prove the following identities: `(sintheta)/(1-costheta)+(tantheta)/(1+costheta)=secthetacos e ctheta+cottheta`

Explanation

To prove the identity

\[ \frac{\sin \theta}{1 - \cos \theta} + \frac{\tan \theta}{1 + \cos \theta} = \sec \theta \cos \theta + \cot \theta \]

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

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