It also accepts an empty string, since you've got a doubled '|' in there. One | separates alternatives, not two.
As for dumbing it down, I'd rewrite it like so:
$A_rx = qr{ \Q $A }x;
$w_rx = qr{ \Q $w }x;
$rx = qr{
$A_rx \s*
\*? \s*
cos \s*
(?:
\( \s* $w_rx \s* \*? \s* t \s* \)
| $w_rx \s* \*? \s* t \s
) \s*
A
}x;
Then you can use it in the following manner:
$string =~ /^\s*($rx)\s*$/.
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