Now I want to use the tangent half-angle formulas:
tan_plus := tan(gamma/2) = sin(gamma)/(1+cos(gamma))
tan_minus := tan(gamma/2) = (1-cos(gamma))/sin(gamma)
How to make FriCAS substitute 1+cos(γ) and 1-cos(γ) in ex2 with
sin(γ)/tan(γ/2) and> sin(γ)tan(γ/2) respectively using
tan_plus and tan_minus?
Of course, you can do that, but I question the WHY.
1+cos(y) and 1-cos(y) look "simpler" to me than the expression with tan.
And note that you want to apply two different rules basically to the
same expression, namely cos(y). How can any CAS figure out that one rule
is for the first cos and the other for the second? You would have to
split the expression and then apply the rules separately and then you
have to put the results together again (but probably boxed so that they
don't change).
If I would now start to figure out how to transform your expression, I
would waste a lot of time. In this case, it is much simpler if you just
enter the substituted expression manually into FriCAS and be done.
Ralf
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