Working on these last questions on my practice exam and I'm pulling my hair out...ha:
Solve the following equations in [0, 2pi]:
(a) sin^2 x + sin x = cos^2 x
I ended up with one solution, x = 3pi/2, wondering if it's ok
(b) sin 2x cos x + cos 2x sin x = 1
This one got me pretty angry but I figure there is simple solution.
I also have an aside: In my solutions manual there was a step that sort of threw me, it was about solving a trigonometric identity and they did something I hadn't seen before, they turned sin^2 x - 3 cos^2 x into sin^2 x + cos^2 x - 4 cos^2 x in order to use the pythagorean identity. So you're allowed to rewrite -3 cos^2 x as cos^2 x - 4cos^2 x? If so it's news to me...
Thanks for any help, it's much appreciated.