I'm trying to solve the following system of equations:
$$l_1 \sin(\alpha) = l_2 \cos(\gamma) + l_3 \sin(\beta)$$
$$l_2 \sin(\gamma) + l_1 \cos(\alpha)=l_3 \cos(\beta) + l_4$$
with the unknowns $\beta, \gamma \in \Bbb R⁺$, the constants $l_1$, ..., $l_4$ $\in$ $\Bbb R⁺$ and the(known) variable $\alpha \in [0,\pi]$.
What I need is a function $\beta(\alpha)$. $\gamma$ is not of any importance to me.
I tried solving this system of equations with Maxima (software), but I don't get any results:
declare(l_1,real);
assume(l_1>=0);
declare(l_2,real);
assume(l_2>=0);
declare(l_3,real);
assume(l_3>=0);
declare(l_4,real);
assume(l_4>=0);
declare(A,real);
assume(A>=0, A<=%pi);
declare(B,real);
assume(B>=0);
declare(G,real);
assume(G>=0);
eq1: l_1*sin(A)=l_2*cos(G)+l_3*sin(B);
eq2: l_2*sin(G)+l_1*cos(A)=l_3*cos(B)+l_4;
solve([eq1, eq2], [B, G]);
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Does anybody know how to solve this, so that I end up with a function $\beta(\alpha)$? Thanks for your help!