Find zeros of this function: $$(3\tan(x)+4\cot(x))\cdot\sin(2x)$$
Do I have to multiply them and solve, or one by one, like:
$$(3\tan(x)+4\cot(x))=0$$and$$\sin(2x)=0.$$

Either way you should get the same answer because Mathematically the equations are still the same. Having said that, the way you've written down as one by one makes it a lot easier because identifying the zeros of a smaller expression is generally easier. 
