$\text{a)}$  

$L=\frac{{\sin }^{3}x+\sin 3x}{{\cos }^{3}x-\cos 3x}=\frac{{\sin }^{3}x+\sin \left(2x+x\right)}{{\cos }^{3}x-\cos \left(2x+x\right)}=$  

$=\frac{{\sin }^{3}x+\sin 2x\cos x+\cos 2x\sin x}{{\cos }^{3}x-\cos 2x\cos x+\sin 2x\sin x}=$  

$=\frac{{\sin }^{3}x+2\sin x{\cos }^{2}x+\left(1-2{\sin }^{2}x\right)\sin x}{{\cos }^{3}x-\left(1-2{\sin }^{2}x\right)\cos x+2{\sin }^{2}x\cos x}=$