Originally Posted by
oryxncrake How can I find the general solutions to the following equations where 0 < x < 2pi?
2cos^2x + cosx = 1
$\displaystyle \textcolor{red}{2\cos^2(x) + \cos(x) - 1 = 0}
$
$\displaystyle \textcolor{red}{[2\cos(x) - 1][\cos(x) + 1] = 0}$
set each factor = 0 and solve for cosx ... solutions for x will be unit circle values
2tanx + square root of 12 = 0
$\displaystyle \textcolor{red}{2\tan(x) + 2\sqrt{3} = 0}$
$\displaystyle \textcolor{red}{\tan(x) = -\sqrt{3}}$
look for solutions on your unit circle