Question

Solve the following equation:
$3{\sin }^{2}2x+7\cos 2x-3=0.$

Answer 1

$3(1-{\cos }^{2}2x)+7\cos 2x=3$

Let $\cos 2x=z.$

${3z}^2=7z$

$z=\frac{7}{3}$ or $z=0.$

So, $z=0,\cos 2x=0,x=(2n+1)\frac{\pi }{8}.$