Question

Find the solution of
(i) $10{\cos }^{3}x-16\cos x=3\cos 2x+3$, in the interval $[-\pi ,\pi ]$
(ii)$2(\cos x+\cos 2x)+\sin 2x(1+2\cos x)=2\sin x$ in the interval $[-\pi ,\pi ]$.

Answer 1

Apply identity of $\cos 2A=2{\cos }^{2}A-1$ and $\sin 2A=2\sin A\cos A$ and solve for $\cos x$