How can i rearrange expressions?

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I have 3 expressions D S L that depends on X Y Z a b
what function can i use to rearrange them to X Y Z that depends on D S L a b
i.e.
input:
D = -(X*cos(a)+Z*sin(a))*cos(b) - Y*sin(b);
S = (X*cos(a)+Z*sin(a))*sin(b) - Y*cos(b);
L = X*sin(a) - Z*cos(a);
output:
X = f(D,S,L,a,b)
Y = f(D,S,L,a,b)
Z = f(D,S,L,a,b)

采纳的回答

DGM
DGM 2021-11-2
Consider:
syms a b D S L X Y Z
e1 = D == -(X*cos(a)+Z*sin(a))*cos(b) - Y*sin(b);
e2 = S == (X*cos(a)+Z*sin(a))*sin(b) - Y*cos(b);
e3 = L == X*sin(a) - Z*cos(a);
S = solve([e1 e2 e3],[X Y Z]);
% observe results
S.X
ans = 
S.Y
ans = 
S.Z
ans = 

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