Question

Solve $6{\sin }^{2}x+2{\sin }^{2}2x=5$.

Answer 1

$6s^2+2\cdot 4s^2{c}^2=5$
or $6s^2+8s^2(1-s^2)=5$
or $8s^4-14s^2+5=0$
$\therefore (4s^2-5)(2s^2-1)=0$
$\therefore s^2=\frac{1}{2}$ or $\frac{5}{4}$
$\therefore \sin \theta =\pm \frac{1}{\sqrt{2}}$
$\therefore \theta =n\pi \pm \frac{\pi }{4}$, $2$nd value rejected.