How to perform this kind of equivalent transformation for trigonometric functions?

Questions
,
1

-Sin[[Pi]/4 - 2 x]

How can I convert the trig function above into the equivalent form below?

Sin[-(\[Pi]/4) + 2 x]

The simplification approach below doesn’t yield the desired result.

-Sin[\[Pi]/4 - 2 x] // FullSimplify
2

The problem is that Mathematica has a built-in (and easily disabled) automatic simplification mechanism.

   expr = -Sin[Pi/4 - 2 x];
   expr /. -Sin[a_] :> Inactive[Sin][-a]

   (*Inactive[Sin][-(\[Pi]/4) + 2 x]*)

  % // Activate

    (*-Sin[\[Pi]/4 - 2 x]*)

  expr = -Sin[Pi/4 - 2 x];
  expr /. -Sin[a_] :> With[{abc = Expand[-a]}, HoldForm[Sin[abc]]]
 
  (*HoldForm[Sin[-(Pi/4) + 2*x]]*)

  % // ReleaseHold

  (*-Sin[\[Pi]/4 - 2 x]*)

Regards M.I.

3

Interesting, the behaviour of Sin depends on the alphabetical order of the variables:

Sin[-a + b]
Sin[-b + a]
Sin[-(\[Pi]/4) + 2 a]