I started to play around with maxima, and there are strange things that
happen (I used a clean maxima as far as I can see):
11111111111111111111111111111111111111111111111111111111111111111
(C1) solve((COS(b)^2*SINH(b)^2-TAN(a)^2*COSH(b)^2*SIN(b)^2)^2,a);
SOLVE is using arc-trig functions to get a solution.
Some solutions will be lost.
%PI
(D1) [a =------]
2
(C2) b;
(D2) b
111111111111111111111111111111111111111111111111111111111111111111
I asked for b to show that b has no value (and I cleaned up the 2-dim output,
it wouldn't copy well).
222222222222222222222222222222222222222222222222222222222222222222
(C3) solve(tan(a)=b,a);
SOLVE is using arc-trig functions to get a solution.
Some solutions will be lost.
(D3) [a = ATAN(b)]
(C4) solve(tan(a)=sin(b),a);
(D4) [SIN(a) = COS(a) SIN(b)]
222222222222222222222222222222222222222222222222222222222222222222
Why's that? The manual says
In the case where E is a
polynomial in some function of the variable to be solved for, say
F(X), then it is first solved for F(X) (call the result C), then
the equation F(X)=C can be solved for X provided the inverse of
the function F is known.
so why wouldn't maxima do in C4 what it did in C3?
3333333333333333333333333333333333333333333333333333333333333333333
(C5) solve([%E^a*COS(b) = SIN(a)*COSH(b),%E^a*SIN(b) =
COS(a)*SINH(b),SIN(a)^2+COS(a)^2 = 1],[exp(a),sin(a),cos(a)]);
a %R1 COS(b) %R1 SIN(b)
(D5) [[%E = %R1, SIN(a) = ----------, COS(a) = ----------------]]
COSH(b) SINH(b)
3333333333333333333333333333333333333333333333333333333333333333333
???????????
Jurgen