Question : If $\sin ^2 \theta-3 \sin \theta+2=0$, then find the value of $\theta\left(0^{\circ} \leq \theta \leq 90^{\circ}\right)$.
Option 1: 45°
Option 2: 0°
Option 3: 60°
Option 4: 90°
Correct Answer: 90°
Solution :
Given, $\sin ^2 \theta-3 \sin \theta+2=0$
⇒ $(\sin \theta - 1)(\sin \theta- 2)=0$
⇒ $\sin\theta=1$ or $\sin\theta=2$
Since $\left(0^{\circ} \leq \theta \leq 90^{\circ}\right)$,
⇒ $\sin \theta=1$
⇒ $\theta = 90^{\circ}$
Hence, the correct answer is $90^{\circ}$.
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