Let S = θ ∈ - 2 π , 2 π : 2 cos 2 θ + 3 sin θ = 0 . Then the sum of the elements of S is:

The given equation 2 cos 2 θ + 3 sin θ = 0 can be written as 2 1 - sin 2 θ + 3 sin θ = 0 ⇒ 2 s i n 2 θ - 3 s i n θ - 2 = 0 ⇒ 2 sin θ + 1 sin θ - 2 = 0 ⇒ sin θ = 2 , - 1 2 , sin θ ≠ 2 ⇒ sin θ = - 1 2 Hence, solutions in - 2 π , 2 π are - π + π 6 , - π 6 , π + π 6 , 2 π - π 6 Sum of the elements is = 2 π .

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Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minPYQ_2019

MathematicsMediumsingle choice

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:

Options:

Answer:

Solution:

The given equation $2 \cos^{2} θ + 3 \sin θ = 0$ can be written as

$2 (1 - \sin^{2} θ) + 3 \sin θ = 0$

$\Rightarrow 2 {s i n}^{2} θ - 3 s i n θ - 2 = 0$

$\Rightarrow (2 \sin θ + 1) (\sin θ - 2) = 0$

$\Rightarrow \sin θ = 2, - \frac{1}{2}, (\sin θ \neq 2)$

$\Rightarrow \sin θ = - \frac{1}{2}$

Hence, solutions in $[- 2 π, 2 π]$ are
$- π + \frac{π}{6}, - \frac{π}{6}, π + \frac{π}{6}, 2 π - \frac{π}{6}$

Sum of the elements is $= 2 π .$

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2019

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