SATHEE: Trigonometrical Equations 3 Question 13

Trigonometrical Equations 3 Question 13

14. The set of all $x$ in the interval $[0, π]$ for which $2 \sin^{2} x - 3 \sin x + 1 \geq 0$ , is…… .

(1987, 2M)

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Answer:

Correct Answer: 14. $x \in 0, \frac{π}{6} \cup \frac{π}{2} \cup \frac{5 π}{6}, π$

Solution:

Given, $2 \sin^{2} x - 3 \sin x + 1 \geq 0$

$\begin{array}{lr} \Rightarrow & 2 \sin^{2} x - 2 \sin x - \sin x + 1 \geq 0 \\ \Rightarrow & (2 \sin x - 1) (\sin x - 1) \geq 0 \\ \Rightarrow & 2 \sin x - 1 \leq 0 or \sin x \geq 1 \\ \Rightarrow & \sin x \leq \frac{1}{2} or \sin x = 1 \\ \Rightarrow & x \in 0, \frac{π}{6} \cup \frac{π}{2} \cup \frac{5 π}{6}, π \end{array}$

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Trigonometrical Equations 3 Question 13

14. The set of all x in the interval [0,π] for which 2sin2⁡x−3sin⁡x+1≥0, is…… .

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14. The set of all $x$ in the interval $[0, π]$ for which $2 \sin^{2} x - 3 \sin x + 1 \geq 0$ , is…… .