Mathematics

This problem asks you to find where two sine waves cancel each other out. The key insight is to use the sum-to-product formula to combine $\sin 5x + \sin 3x$ into a single product, which equals zero when either factor is zero. This transforms a tricky trigonometric equation into two simpler ones you can solve separately, then count solutions carefully within the given interval.

This problem asks you to find where two sine waves cancel each other out. The key insight is to use the sum-to-product formula to combine $\sin 5x + \sin 3x$ into a single product, which equals zero when either factor is zero. This transforms a tricky trigonometric equation into two simpler ones you can solve separately, then count solutions carefully within the given interval.