Prove the trig identity: 1+cos x/sin x = csc x + cot x

1. Start with the right-hand side of the equation: \csc x + \cot x

2. Express \csc x and \cot x in terms of sine and cosine:
\csc x = \frac{1}{\sin x}
\cot x = \frac{\cos x}{\sin x}

3. Add the fractions:
\csc x + \cot x = \frac{1}{\sin x} + \frac{\cos x}{\sin x} = \frac{1 + \cos x}{\sin x}

4. The expression \frac{1 + \cos x}{\sin x} matches the left-hand side of the identity.

Therefore, the identity is valid:

\frac{1 + \cos x}{\sin x} = \csc x + \cot x