Start by getting everything on the same side of the equals sign and then set it equal to 0. [tex]tan^2xsinx-tan^2x=0[/tex]. Factor out the common tan^2x like this: [tex]tan^2x(sinx-1)=0[/tex]. Now we have 2 separate equations to solve: [tex]tan^2x=0[/tex] and sinx = 0. Now we have to figure out where tan^2 is 0 between 0 and 2pi. If we include 2pi, the solutions for that equation are [tex]x = 0, \pi , 2 \pi [/tex]. You can test those out on your calculator just to be sure. There's only one value of x for the next equation. The only place between 0 and 2pi where the sin x = 1 is at x = [tex] \frac{ \pi }{2} [/tex]. And there you go!
