1. The problem statement, all variables and given/known data Determine all points on the function [itex]y=\sin2x-2sinx[/itex] where the tangent is parallel to the x-axis. 2. Relevant equations f'(sin(x)) = cos(x) chain rule: f'(f(g(x)) = g'f + f'g 3. The attempt at a solution [tex]y=sin2x-2sinx[/tex] [tex]y\prime=cos(2x)(2)-[2cosx+0sinx][/tex] [tex]y\prime=cos(2x)(2)-2cosx[/tex] If I multiply 2 and cos(2x), do I get 2cos(2x) or do I get 2cos(4x)? Is there a way to simplify it further by subtracting the -2cosx? Do I use the sum and difference identities? My trig is still pretty rusty :( In a similar question without trig, we'd derive the equation, and factor it to find out the points of x; but I'm not quite sure how to do this :( Thanks for the help.