We were given the equation $$\cos x \cos 7x = \cos 5x \cos 3x.$$ How can we solve it for $x$? So far I have solved only basic trigonometric equations, so I don't know how to reduce it to basic one.
Thanks in advance for some hints on how to solve the equation.
Using the linearisation identity mentioned in a comment, it is equivalent to the equation $\cos 6x=\cos 2x$,. The solutions of the latter satisfy the congruences $$6x\equiv\pm2x\mod 2\pi.$$ Can you end the computations and simplify the results?