Simplify and FullSimplify do not simplify a simple term

Question

Why don't Simplify and FullSimplify work on: $\frac{\sqrt{a + \cos \theta}}{\sqrt{\frac{a + \cos \theta}{1 + a}}}$?

FullSimplify[ Sqrt[a + Cos[\[Theta]]] /Sqrt[(a + Cos[\[Theta]])/(
 1 + a)]]

Even if $\cos \theta \leq 0$ the term should simplify.... no?

Answer 1

You need to give assumptions, try this:

    FullSimplify[ Sqrt[a + Cos[\[Theta]]] /Sqrt[(a + Cos[\[Theta]])/(
 1 + a)], Assumptions->a>1]

or try this:

    Simplify[ Sqrt[a + Cos[\[Theta]]] /Sqrt[(a + Cos[\[Theta]])/(
 1 + a)], Assumptions->a>1]