sin2θ - 3sinθ + 2 = 0, will be true if ?

Answer: Option D

$$\begin{array}{rl}& {\sin }^2\theta -3\sin \theta +2=0\\ & \Rightarrow {\sin }^2\theta -2\text{sin }\theta -\sin \theta +2=0\\ & \Rightarrow \sin \theta \left(\sin \theta -2\right)-1\left(\sin \theta -2\right)=0\\ & \Rightarrow \left(\sin \theta -1\right)\left(\sin \theta -2\right)=0\\ & \left[\because \sin \theta \ne 2\right]\text{Put value of }\\ & \Rightarrow \sin \theta =1\\ & \Rightarrow \text{sin }\theta =\sin 90^{\circ }\\ & \Rightarrow \theta =90^{\circ }\\ & \\ & \mathbf{Alternate}:\\ & \text{Put value of }\theta =90^{\circ }\\ & \left[\text{Take help from the options}\right]\\ & \Rightarrow {\sin }^2\theta -3\sin \theta +2=0\\ & \Rightarrow {\sin }^{2}90^{\circ }-3\text{sin }90^{\circ }+2=0\\ & \Rightarrow 1-3\times 1+2=0\\ & \left[\sin {90}^{\circ }=1\right]\\ & \Rightarrow 0=0\left[\text{matched}\right]\\ & \text{So, this is answer}\text{.}\end{array}$$