2.68: Derivative of a trigonometric quotient and area

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\sin x}{1 + \cos x}\right) = \dfrac{1}{1 + \cos x}$.

The diagram shows part of the graph of $y = \dfrac{1}{1 + \cos x}$. Use the result from part (i) to find the area enclosed by the graph and the lines $x = 0$, $x = 2$ and $y = 0$.