Let S -2 - 2 - 2 cos 2-3 sin-0Then the sum of the elements of S is-A- 13 -6B- 5 -3C- 2 -D- -

The correct option is C 2π2cos^2 θ+ 3 sinθ=0 ⇒ 2 2sin^2 θ+3 sinθ=0 ⇒ 2sin^2 θ 3sinθ 2=0 ⇒ (2sinθ+1)(sinθ 2)=0 ⇒sinθ= 1/2, sinθ=2 [Reject] nbsp; Roots: π+π/ ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

Let S =θ∈[-2 ...

Question

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:

\frac{13 π}{6}

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\frac{5 π}{3}

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π

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π

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Solution

The correct option is C 2 $π$
$2 {cos}^{2} θ + 3 sin θ = 0 \Rightarrow 2 - 2 {sin}^{2} θ + 3 sin θ = 0 \Rightarrow 2 {sin}^{2} θ - 3 sin θ - 2 = 0 \Rightarrow (2 sin θ + 1) (sin θ - 2) = 0 \Rightarrow sin θ = - \frac{1}{2}, sin θ = 2 [R e j e c t] R o o t s : π + \frac{π}{6}, 2 π - \frac{π}{6}, - \frac{π}{6}, - π + \frac{π}{6} ∴ S u m = 2 π$

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Similar questions

Q. 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?

L e t A = {θ \in (- \frac{π}{2}, π) : \frac{3 + 2 i sin θ}{1 - 2 i sin θ} is purely imaginary}

. The sum of all the elements in

A

is :

Q. If

\cos θ + \sqrt{3} \sin θ = 2, then θ =

(a)

π / 3

(b)

2 π / 3

(c)

4 π / 6

(d)

5 π / 12

Q. Let

\frac{- 5 π}{12} \leq θ \leq - \frac{π}{3}

Max. Value of

cos (\frac{π}{6} + θ) - tan (θ + \frac{π}{6}) + tan (θ + \frac{2 π}{3})

Q. The number of solution of pair of equations

2 s i n^{2} θ - c o s 2 θ = 0

and

2 c o s^{2} θ - 3 s i n θ = 0

in the interval

[θ, 2 π]

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Let S={θ∈[−2π,2π]:2cos2θ+3sinθ=0}. Then the sum of the elements of S is:

The correct option is C 2π2cos2θ+3sinθ=0⇒2−2sin2θ+3sinθ=0⇒2sin2θ−3sinθ−2=0⇒(2sinθ+1)(sinθ−2)=0⇒sinθ=−12, sinθ=2 [Reject]Roots:π+π6,2π−π6,−π6,−π+π6∴Sum=2π

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: