(a) If $x \cos(p+y) + \cos p \sin(p+y) = 0$, prove that $\cos p \frac{dy}{dx} = - \cos^2(p+y)$, where $p$ is a constant. OR (b) Find the value of $a$ and $b$ so that function $f$ defined as: $f(x) = \begin{cases} \frac{x-2}{|x-2|} + a, & \text{if } x < 2 \\ a+b, & \text{if } x = 2 \\ \frac{x-2}{|x-2|} + b, & \text{if } x > 2 \end{cases}$ is a continuous function.