<s>[INST] If $x = a( \theta +\sin \theta)$ and $y = a(1-\cos \theta)$ then find $\frac{dy}{dx}$ If $x = a( \theta +\sin \theta)$ and $y = a(1-\cos \theta)$ then $\frac{dy}{dx}$ will be equal to : 
$a) \sin \frac{\theta}{2}$
$b) \cos \frac{\theta}{2}$
$c) \tan \frac{\theta}{2}$
$d) \cot \frac{\theta}{2}$
I have solved till : $\frac{dy}{dx} = \frac{\sin \theta}{1 + \cos \theta}$ using $\frac{dy}{dx} = \frac{dy}{d \theta} . \frac{d \theta}{dx}$. 
How do I reduce to the option's forms?
 [/INST] $$\dfrac{\sin a}{1+\cos a}=\frac{\sin\frac{a}{2}cos\frac{a}{2}}{{\cos^2\frac{a}{2}}} $$
$=\tan\frac{a}{2} $ is the solution
( Rotation of cycloid?)
</s>