You're on a roll — Step 1: Use the double angle identity for $\cos^2 x$. Recall the identity $\cos 2x = 2\cos^2 x - 1$. Rearranging this, we get $\cos^2 x = \frac{1+\cos 2x}{2}$. Substitute this into the first term of the expression: $$ 14\cos^2 x = 14\left(\frac{1+\cos 2x}{2}\right) $$ $$ = 7(1+\cos 2x) $$ $$ = 7 + 7\cos 2x $$ Step 2: Use the double angle identity for $\sin x \cos x$. Recall the identity $\sin 2x = 2\sin x \cos x$. Substitute this into the second term of the expression: $$ -48\sin x \cos x = -24(2\sin x \cos x) $$ $$ = -24\sin 2x $$ Step 3: Combine the transformed terms. Add the results from Step 1 and Step 2: $$ 14\cos^2 x - 48\sin x \cos x = (7 + 7\cos 2x) - 24\sin 2x $$ Rearrange the terms to match the form $A\cos 2x + B\sin 2x + C$: $$ = 7\cos 2x - 24\sin 2x + 7 $$ Step 4: Identify the constants $A$, $B$, and $C$. Comparing $7\cos 2x - 24\sin 2x + 7$ with $A\cos 2x + B\sin 2x + C$: $A = 7$ $B = -24$ $C = 7$ The expression in the required form is $\boxed{7\cos 2x - 24\sin 2x + 7}$. What's next?