This is annoying mathematica.stackexchange.com/questions/265951

@JimB I know that TrigReduce and TrigExpand work. However, this is a small part of a ginormous expression to which I can't apply either, because then the whole expression becomes orders of magnitude larger and Mathematica takes ages to do anything with it, but I don't want to have to go through the expression and replace every occurrence of a trigonometric identity by hand.

@ThunderBiggi Maybe it's a bug. It appears that, if Simplify is added to the transformation functions, it's reduced to 1 but that simplification is rejected. No idea why. Code:

echo = (Print[#1]; #1) &;
Simplify[-(1/4) (Cos[\[Gamma]1]^2 + Sin[\[Gamma]1]^2) (-4 + x1^2 +
    x2^2 + x3^2 + x4^2),
 TransformationFunctions -> {Automatic, echo@Simplify[echo@#] &}]

This works:

echo = (Print[#1]; #1) &;
Simplify[-(1/4) (Cos[\[Gamma]1]^2 + Sin[\[Gamma]1]^2) (-4 + x1^2 +
    x2^2 + x3^2 + x4^2),
 ComplexityFunction -> (Simplify`SimplifyCount[#] +
     5 Count[#, _Cos | _Sin, Infinity] &)]

@MichaelE2 That is interesting. Can somebody check in older version of Mathematica (I am using 13)

Because I don't remember encoutering such terms before in my calcualtions (and I have been doing more or less the same type of stuff for years with Mathematica)

What does your last piece of code do?

I can't check earlier versions...

I don't remember it either.