How can i rearrange expressions?

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)

Answer 1

[DGM]

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 =