Simple Question: How to simplify what is inside the Sin function like below?

Question

I have this code of Mathematica
(1/(2 (fj - fk) π))
 Cos[(fj - fk) π T + (fj - fk) π (T + δt)] Sin[(fj - 
       fk) π T - (fj - fk) π (T + δt)]

There are a few terms inside these Sin functions that if multiplied can be canceled out, Can someone tell me how to simplify this expression in Mathematica? TrigReduce, simply, Fullsimply didn't work here.

mmeent · Accepted Answer

Does this do what you want?
expr=(1/(2 (fj - fk) π)) Cos[(fj - fk) π T + (fj - 
   fk) π (T + δt)] Sin[(fj - fk) π T - (fj - 
   fk) π (T + δt)];
expr /. (f : Cos | Sin)[a_] :>  f[Simplify[a]]

This applies Simplify only to the arguments of Sin and Cos
Alternatively,
Simplify[expr,Trig->False]

(This prevents Mathematica from applying Trig manipulations during Simplify

Simple Question: How to simplify what is inside the Sin function like below?

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