Question

The number of values of $\theta$, where $\theta$ lies in the interval $(0,2\pi )$ satisfying the equation $\left(\sin \theta -2\right)\left(\sin \theta -3\right)=0$

Answer 1

$\left(\sin \theta -2\right)\left(\sin \theta -3\right)=0$

Let $\sin \theta =x$

$\Rightarrow \left(x-2\right)\left(x-3\right)=0$

$\Rightarrow x=2orn=3$

$\Rightarrow \sin \theta =2or\sin \theta =3$

but $\sin \theta \in \left[-1,1\right]$

So , no value of $\theta$ exists which satisfies the given condition