Question

\\\frac{1 - \cos t}{\sin t} = \frac{\sin t}{1 + \cos t}\\

Explanation:

Multiply the numerator and denominator by the conjugate

$$ \frac{1 - \cos t}{\sin t} = \frac{(1 - \cos t)(1 + \cos t)}{\sin t(1 + \cos t)} $$

Apply the Pythagorean identity to simplify the numerator

$$ \frac{1 - \cos^2 t}{\sin t(1 + \cos t)} = \frac{\sin^2 t}{\sin t(1 + \cos t)} $$

Cancel the common factor of sine

$$ \frac{\sin t}{1 + \cos t} $$

Answer:

$$\frac{1 - \cos t}{\sin t} = \frac{\sin t}{1 + \cos t}$$