Prove that $$16\cos^5A-20\cos^3A+5\cos A=\cos5A$$
My solution begins here; $$ \begin{align} \text{RHS} & =\cos5A \\ & =\cos(A+4A) \\ & =\cos A\cos4A-\sin A\sin4A \\ & =\cos A(2\cos^2 2A-1)-\sin A(2\sin2A\cos2A) \\ & =2\cos A\cos^2 2A-\cos A-2\sin A\sin2A\cos2A \\ & =2\cos A\cos^2 2A-\cos A-2\sin A(2\sin A\cos A)\cos2A \end{align} $$ Now how do I move on?