Mathematics

This problem asks you to solve a trigonometric equation by recognizing a difference of cosines—a perfect setup for the sum-to-product formula. Rather than expanding $\cos 2x$ and $\cos 6x$ separately, rewrite the equation as a product of sines, which factors nicely and gives you simpler equations to solve. Once you have those factors equal to zero, you'll find all the angles in the given interval.

This problem asks you to solve a trigonometric equation by recognizing a difference of cosines—a perfect setup for the sum-to-product formula. Rather than expanding $\cos 2x$ and $\cos 6x$ separately, rewrite the equation as a product of sines, which factors nicely and gives you simpler equations to solve. Once you have those factors equal to zero, you'll find all the angles in the given interval.