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Need to Simplify Trig Functions of ArcTan

This works

In[24]:= Cos[ArcTan[x, y]] // TrigReduce
Out[24]= x/Sqrt[x^2 + y^2]

In[25]:= Sin[ArcTan[x, y]] // TrigReduce
Out[25]= y/Sqrt[x^2 + y^2]

but 

In[26]:= Cos[3/4 ArcTan[x, y]] // TrigReduce
Out[26]= Cos[3/4 ArcTan[x, y]]

In[52]:= Sin[3/4 ArcTan[x, y]] // TrigReduce
Out[52]= Sin[3/4 ArcTan[x, y]]

How can I get these expressions in terms of x and y ?
POSTED BY: Frank Kampas
2 Replies
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POSTED BY: Frank Kampas

Maybe:

 {FullSimplify[Cos[3/4 ArcTan[x, y]] // TrigToExp, 
   Assumptions -> {x > 0, y > 0}], 
  FullSimplify[Sin[3/4 ArcTan[x, y]] // TrigToExp, 
    Assumptions -> {x > 0, y > 0}] // Expand}

(*{((x + I y)^(3/2) + (x^2 + y^2)^(3/4))/(
 2 (x + I y)^(3/4) (x^2 + y^2)^(
  3/8)), -((I (x + I y)^(3/4))/(2 (x^2 + y^2)^(3/8))) + (
  I (x^2 + y^2)^(3/8))/(2 (x + I y)^(3/4))}*)
POSTED BY: Mariusz Iwaniuk
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