Question
Solve : $\sin^2\theta - 3 \sin \theta + 2 = 0 .$
✓
Answer
$\sin^2\theta - 3 \sin \theta + 2 = 0$
$\Rightarrow \sin^2\theta - 2 \sin \theta - \sin \theta + 2 = 0$
$\Rightarrow \sin \theta (\sin \theta - 2) - 1(\sin \theta - 2) = 0$
$\Rightarrow (\sin \theta - 2)(\sin \theta - 1) = 0$
$\Rightarrow \sin \theta - 2 = 0$
$\Rightarrow \sin \theta = 2 \sin \theta = 2$ has no solution for angle $\theta$ , as there is no any angle whose $\sin \theta$ is equal to $2.$
$\Rightarrow \sin \theta - 1 = 0$
$\Rightarrow \sin \theta = 1$
$\Rightarrow \theta = 90^\circ$
$\Rightarrow \sin^2\theta - 2 \sin \theta - \sin \theta + 2 = 0$
$\Rightarrow \sin \theta (\sin \theta - 2) - 1(\sin \theta - 2) = 0$
$\Rightarrow (\sin \theta - 2)(\sin \theta - 1) = 0$
$\Rightarrow \sin \theta - 2 = 0$
$\Rightarrow \sin \theta = 2 \sin \theta = 2$ has no solution for angle $\theta$ , as there is no any angle whose $\sin \theta$ is equal to $2.$
$\Rightarrow \sin \theta - 1 = 0$
$\Rightarrow \sin \theta = 1$
$\Rightarrow \theta = 90^\circ$
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