I did get the right answers, but I still would like to make sure my thinking is accurate, and also check if I made unnecessary calculations somewhere.

Get all the solutions to the trigonometric equation

in the interval [0, 2pi[

What I did was:

We set u = cos^2 and get

which gives us u = 0 and u = 1.

cos^2 x = 0 gives us cos x = +/- 0. x = pi/2 + k(pi).

cos^2 x = 1 gives us cos x = +/- 1. x = 0 + k(pi).

So the solutions are, in order,

0, pi/2, pi, 3pi/2.

I apologize for the mix and match between Latex and regular text.