Trying a new in 12.2 command `FunctionInjective`

, I execute

```
FunctionInjective({Sin(x)^2, Element(x, Integers)}, x)
```

`False`

and

```
FunctionInjective({Cos(x)^2, Element(x, Integers)}, x)
```

`True`

Both function are even on the reals, so both outputs should be `False`

as the output of

```
DiscretePlot(Cos(x)^2, {x, -8, 8})
```

shows,

How to explain this difference?

I try to present `Cos(x)^2`

as `Sin(Pi/2 - x)^2`

and `(1+Cos(2x))/2`

, but

the outputs of

```
FunctionInjective({Sin(Pi/2 - x)^2, Element(x, Integers)}, x)
```

and

```
FunctionInjective({(Cos(2*x) + 1)/2, Element(x, Integers)}, x)
```

still are `True`

.