Question

Show that the equation \[2\tan^2 \theta \cos \theta=3 \]can be written in the form \[2\cos^2 \theta + 3 \cos \theta -2 =0\]

Answer 1

maybe start with
\[2\tan^2(x)=2\frac{\sin^2(x)}{\cos^2(x)}=\frac{2(1-\cos^2(x)}{\cos^2(x)}\] and then algebra should do it