| Author |
Comment/Response |
Bill Simpson
|
 05/28/12 6:42pm
For sufficiently small and simple a and b.
In[1]:= Simplify[a=5;b=3;Reduce[a*Sin[a x]-b*Sin[b x]==0,x]]
Out[1]= C[1] ∈ Integers && (x == 2*Pi*C[1] || Pi + 2*Pi*C[1] == x || x + 2*ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 1, 0]]] ==
2*Pi*C[1] || x == 2*(ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 1, 0]]] + Pi*C[1]) ||
x + 2*ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 2, 0]]] == 2*Pi*C[1] ||
x == 2*(ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 2, 0]]] + Pi*C[1]) ||
x + 2*ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 3, 0]]] == 2*Pi*C[1] ||
x == 2*(ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 3, 0]]] + Pi*C[1]) ||
x + 2*ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 4, 0]]] == 2*Pi*C[1] ||
x == 2*(ArcTan[Sqrt[Root[1 - 18*#1 + 42*#1^2 - 18*#1^3 + #1^4 & , 4, 0]]] + Pi*C[1]))
In[2]:= ToRadicals[Root[1-18 #1+42 #1^2-18 #1^3+ #1^4&,1]]
Out[2]= 9/2+Sqrt[41]/2-Sqrt[(59+9*Sqrt[41])/2]
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