| Author |
Comment/Response |
Bill Simpson
|
 10/11/12 02:15am
Mathematica usually uses LeafCount to decide which of two alternatives is "simpler", smaller count means simpler.
In[1]:= LeafCount[a*Sin[x]+b*Cos[x]]
Out[1]= 9
In[2]:= LeafCount[Sqrt[a*b]*Sin[x+c]]
Out[2]= 12
So Mathematica thinks your preferred form is more complicated. That means something more than Simplify will be needed.
Here is one method you might use
In[3]:= a*Sin[x]+b*Cos[x]/.a_*Sin[x_]+b_*Cos[x_]->Sqrt[a*b]*Sin[x+c]
Out[3]= Sqrt[a*b]*Sin[c + x]
This even works when you do not literally have a,b,x, but the same variable or constant must appear on both your x positions.
In[4]:= 7*Sin[q]+3*Cos[q]/.a_*Sin[x_]+b_*Cos[x_]->Sqrt[a*b]*Sin[x+c]
Out[4]= Sqrt[21]*Sin[c + q]
You might want to enhance this by using the appropriate expression for c as a function of a and b.
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