I have a question when solving trigonometric equations. For example: Find all the solutions in the interval [0,2pi) [tex]\sin \theta \tan \theta = \sin \theta \][/tex] If you choose to divide through by [tex]\sin \theta\][/tex] we get, [tex]\tan \theta = 1\][/tex] such that [tex]\sin \theta \ne 0\][/tex] otherwise we are essentially dividing both sides by zero, which we cannot do. Do we need to be careful when solving trigonometric equations using multiplication and division? We're dividing by a term that can take on the value of zero. Does this have any special name? How can I learn more about this? Are there any techniques to use when solving trig equations so this doesn't happen?