I have the following expression
$$
\frac{4 \sin(a)}{\sin(a)^2 + \cos(a)^2 + r^4 \sin(a)^4\cos(a)^2 \sin(b)^2 \cos(b)^2 }
$$
I would like Mathematica to recognize that this expression can be simplified to
 $$
\frac{4\sin(a)}{1+\frac{1}{4}r^4\sin(a)^4\cos(a)^2\sin(2b)^2} \ \ (1)
$$
But although I can do the following

```
FullSimplify[Cos[a]^2 + Sin[a]^2]
=> 1

```

and

```
FullSimplify[Cos[b]^2 Sin[b]^2, ComplexityFunction -> Length]
=> 1/4 Sin[2 b]^2

```

when I try to use FullSimplify on the whole expression it will give me

```
FullSimplify[(4 Sin[a])/(Cos[a]^2 + Sin[a]^2 + r^4 Cos[a]^2 Cos[b]^2 Sin[a]^4 Sin[b]^2)]
=> (4 Sin[a])/(Sin[a]^2 + Cos[a]^2 (1 + r^4 Cos[b]^2 Sin[a]^4 Sin[b]^2))

```

What can I do to transform my fraction into the form $(1)$ ?