Question: Please help in Solving the Trigonometric Equation:

$$\cos^2x - \sin^2x = \cos3x$$

Answer: 
$$
\cos 3x=\cos x \cos x - \sin x \sin x= \cos 2x,
$$
which is equivalent to
$$
3x\pm 2x = 2k\pi
$$
for some integer $k$.
**Hint:** Use the trigonometry identity for the $\cos 2\theta$.