Question

Solve 2cos^2x+3cosx-2=0

Answer 1

$\bf 2cos^2(x)+3cos(x)-2=0\impliedby \textit{so, notice is just a quadratic} \\\\\\\ [2cos(x)~~-~~1][cos(x)~~+~~2]=0\\\\ -------------------------------\\\\ 2cos(x)-1=0\implies 2cos(x)=1\implies cos(x)=\cfrac{1}{2} \\\\\\ \measuredangle x=cos^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}\\\\ -------------------------------\\\\ cos(x)+2=0\implies cos(x)=-2$

now, for the second case, recall that the cosine is always a value between -1 and 1, so a -2 is just a way to say, such angle doesn't exist.