Question

The general value of $\theta$ satisfying $si{n}^2\theta +sin\theta =2$ is

• A. $n\pi (-1{)}^n\frac{\pi }{6}$
• B. $2n\pi +\frac{\pi }{4}$
• C. $n\pi +(-1{)}^n\frac{\pi }{2}$
• D. $n\pi +(-1{)}^n\frac{\pi }{3}$

Answer 1

The correct option is C $n\pi +(-1{)}^n\frac{\pi }{2}$

$si{n}^2\theta +sin\theta =2$
$\Rightarrow \sin \theta =\frac{-1\pm \sqrt{9}}{2}=-2,1$
$\Rightarrow \sin \theta \ne -2$ or $\sin \theta =1$
$\Rightarrow \theta =n\pi +{(-1)}^n\frac{\pi }{2}$