$$10x=\sin^{-1}(38y)-\sin^{-1}(52y)$$
$$40x=\sin^{-1}(-53y)-\sin^{-1}(52y)$$
Multiplying across the first equation by $4$ and subtracting the equations gives:
$$4\sin^{-1}(38y)-3\sin^{-1}(52y)-\sin^{-1}(-53y)=0$$
I found a formula for adding inverse sine functions but only if the coefficients were similar.
How would I solve for $y$ in this expression ?