Mathematics - Trigonometric Equation Question with Solution | TestHub

$$\begin{array}{rl}& \text{ As, }2{\sin }^2\theta -5\sin \theta +2>0\\ & \Rightarrow (2\sin \theta -1)(\sin \theta -2)>0\\ & [\text{ where, }(\sin \theta -2)<0\text{ for all }\theta \in R]\\ & \therefore (2\sin \theta -1)<0\end{array}$$
$$\begin{array}{ll}\Rightarrow & \sin \theta <\frac{1}{2},\text{ shown as }\\ \therefore & \theta \in \left(0,\frac{\pi }{6}\right)\cup \left(\frac{5\pi }{6},2\pi \right)\end{array}$$