Okay, the equation is sin 4x = -2 sin 2x. I manipulate and rearrange the equation to acquire 2 sin 2x(cos 2x + 1) = 0. I set each factor to zero, but come across a problem when setting the factor 2 sin 2x to zero. How I did, which was different from the answer key, was take the angle that makes sin 2x = 0, which was 0, and add 2npi.
So: 2x = 0 + 2npi ---> x = npi. But they have x = (n/2)pi, giving them two more angles than I had produced--which were 0 and pi. Why did they do that? They want me to find all of the angles on the interval [0, 2pi)