6.8 Advanced Topic: Transforming Trigonometric Expressions
As earlier sections have shown, even when you restrict yourself to polynomials and rational expressions, there are many different ways to write any particular expression. If you consider more complicated expressions, involving, for example, higher mathematical functions, the variety of possible forms becomes still greater. As a result, it is totally infeasible to have a specific function built into Mathematica TE to produce each possible form. Rather, Mathematica TE allows you to construct arbitrary sets of transformation rules for converting between different forms. Many Mathematica TE packages include such rules; the details of how to construct them for yourself are given in Chapter 28.
Under normal conditions, Expand leaves trigonometric functions unchanged.
In[1]:= Expand[Sin[x]^2 + Sin[2x]^2]
Out[1]= 
