Use the double angle identity for ^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:

Recall the identity $\sin 2x = 2\sin x \cos x$.
Substitute this into the second term of the expression:

Add the results from Step 1 and Step 2:

Rearrange the terms to match the form $A\cos 2x + B\sin 2x + C$:

Comparing $7\cos 2x - 24\sin 2x + 7$ with $A\cos 2x + B\sin 2x + C$:
$A = 7$
$B = -24$
$C = 7$