Question

Solve the following equation:
$2{\cos }^{2}x+4\cos x=3{\sin }^{2}x$

Answer 1

${2\cos }^{2}x+4\cos x={3\sin }^{2}x$

${2\cos }^{2}x+4\cos x=3(1-{\cos }^2)$

$\cos x=\frac{-4\pm \sqrt{4^2-4\times 5\times (-3)}}{2\times 5}$

$\cos x=\frac{-4\pm \sqrt{16+60}}{10}=\frac{-4\pm \sqrt{76}}{10}$

So, let $\cos x=\frac{-4\pm \sqrt{76}}{10}=p$

$\therefore$ $x=2n\pi \pm {\cos }^{-1}\left(p\right)$