I get trig expressions which are long but contain structure, The simplest example might be the following which is nothing but a.b where a and b are two unit vectors in polar coordinates.
Whereas the above is easy to identify, in general the structures are not evident.
Question 1 Is there a way to extract such vectors from long trig expressions? I am most interested in identifying inner, cross and outer products of unit vectors contained in these expressions.
Question 2 I would like to apply trig formulae, double angles etc, selectively. That is apply the formula to only some of the quantities present, say only on the angles theta;a, and theta;b, but not on the phi's. How is that done?