SATHEE: Trigonometrical Equations 1 Question 3

Trigonometrical Equations 1 Question 3

3. Let S= { $θ \in [- 2 π, 2 π] : 2 \cos^{2} θ + 3 \sin θ = 0$ }, then the sum of the elements of $S$ is

(2019 Main, 9 April I)

(a) $2 π$

(b) $π$

(d) $\frac{13 π}{6}$

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Answer:

Correct Answer: 3. (a)

Solution:

We have, $θ \in [- 2 π, 2 π]$

$\begin{aligned} and 2 \cos^{2} θ + 3 \sin θ = 0 \\ \Rightarrow 2 (1 - \sin^{2} θ) + 3 \sin θ = 0 \\ \Rightarrow 2 - 2 \sin^{2} θ + 3 \sin θ = 0 \\ \Rightarrow 2 \sin^{2} θ - 3 \sin θ - 2 = 0 \\ \Rightarrow 2 \sin^{2} θ - 4 \sin θ + \sin θ - 2 = 0 \\ \Rightarrow 2 \sin θ (\sin θ - 2) + 1 (\sin θ - 2) = 0 \\ \Rightarrow (\sin θ - 2) (2 \sin θ + 1) = 0 \\ ∴ \sin θ = \frac{- 1}{2} \\ [∵ (\sin θ - 2) \neq 0] \\ ∴ θ = 2 π - \frac{π}{6}, - π + \frac{π}{6}, - \frac{π}{6}, π + \frac{π}{6} \\ [∵ θ \in [- 2 π, 2 π]] \end{aligned}$

Now, sum of all solutions

$= 2 π - \frac{π}{6} - π + \frac{π}{6} - \frac{π}{6} + π + \frac{π}{6} = 2 π$

Trigonometrical Equations 1 Question 3

3. Let S= { $θ \in [- 2 π, 2 π] : 2 \cos^{2} θ + 3 \sin θ = 0$ }, then the sum of the elements of $S$ is

Answer:

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Trigonometrical Equations 1 Question 3

3. Let S= {θ∈[−2π,2π]:2cos2⁡θ+3sin⁡θ=0}, then the sum of the elements of S is

Answer:

Engineering Preparation

Medical Preparation

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Sample Mock Test

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NCERT Exercise Video Solution

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3. Let S= { $θ \in [- 2 π, 2 π] : 2 \cos^{2} θ + 3 \sin θ = 0$ }, then the sum of the elements of $S$ is