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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)]

enter image description here

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.

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  • $\begingroup$ I encounter many equations like this that I need to solve $\endgroup$
    – good_omen92
    Commented Oct 15, 2020 at 12:40
  • $\begingroup$ Are you aware of functions like TrigReduce, TrigExpand, TrigToExp, and ExpToTrig? $\endgroup$
    – TimRias
    Commented Oct 15, 2020 at 12:46
  • $\begingroup$ Yes but my application is different, I want this exact equation for representation purpose so I want Mathematica to simply what is inside this cos and sin for me. The above function changes everything by giving it another shape.@mmeent $\endgroup$
    – good_omen92
    Commented Oct 15, 2020 at 12:49
  • 1
    $\begingroup$ tried Simplify? $\endgroup$
    – kglr
    Commented Oct 15, 2020 at 12:53

1 Answer 1

Reset to default
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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

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  • $\begingroup$ I have expertise in wireless communication and I only know MATLAB, has no idea how you did this? Can you do the same for cos term, like both sin and cos? $\endgroup$
    – good_omen92
    Commented Oct 15, 2020 at 12:57
  • $\begingroup$ Why not simplify the whole expression using SImplify["your expression"] $\endgroup$
    – Daniel Huber
    Commented Oct 15, 2020 at 15:00
  • $\begingroup$ @DanielHuber Because the OP has indicated that they want to keep the overall functional form of the expression. (By default, Simplify will re-express the given expression as a sum of two trig functions rather than the product as given.) $\endgroup$
    – TimRias
    Commented Oct 15, 2020 at 15:04

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