Question

Solve
$7{\sin }^2\theta +3{\cos }^2\theta =4$

Answer 1

$7{\sin }^2\theta +3{\cos }^2\theta =4$

$7-7{\cos }^2\theta +3{\cos }^2\theta =4$

$⟹4{\cos }^2\theta =3$

$⟹{\cos }^2\theta =(\frac{\sqrt{3}}{2}{)}^2$

The general solution of $\theta$ is $n\pi \pm \frac{\pi }{6}$