If -3cos2- -2-3sin-cos- -3sin2- -0- then

The correct option is B None of the above √( 3 )cos ^ 2 θ #160; 3√( 3 )sinθ #160; cosθ #160; +sinθ #160; cosθ #160; 3sin ^ 2 θ #160; ...

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Byju's Answer

Standard XII

Mathematics

Domain

If √3cos2θ ...

Question

If $\sqrt{3} {cos}^{2} θ - 2 \sqrt{3} sin θ cos θ - 3 {sin}^{2} θ = 0$ , then

θ = n π + \frac{π}{6}, n \in l

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θ = π n + \frac{π}{6}, n \in l

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θ = n π + \frac{π}{3}, n \in l

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N o n e o f t h e a b o v e

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Solution

The correct option is B $N o n e o f t h e a b o v e$
$\sqrt{3} {cos}^{2} θ - 3 \sqrt{3} sin θ cos θ + sin θ cos θ - 3 {sin}^{2} θ = 0$
$\sqrt{3} cos θ (cos θ - 3 sin θ) + sin θ (cos θ - 3 sin θ) = 0$
$(cos θ - 3 sin θ) (\sqrt{3} cos θ + sin θ) = 0$
$tan θ = \frac{1}{3}$
Or, $tan θ = - \sqrt{3}$
So, $θ = n π + {tan}^{- 1} (\frac{1}{3})$
Or $θ = n π - \frac{π}{3}$

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Similar questions

Q. If

| 2 sin θ - cosec θ | \geq 1

, then complete set of values of

θ

is
(where

n \in Z

)

Consider the system of linear equations in x, y and z ;
(sin 3 $θ$ ) x - y + z = 0 ......(i)
(cos 2 $θ$ )x + 4y + 3z = 0 ......(ii)
2x + 7y+ 7z = 0 ......(iii)

The value of $θ$ for which the system has nontrivial solution is

List-I	List-II
$1) {tan}^{2} θ = 1$	a $) n π \pm π / 6$
$2) {cos}^{2} θ = \frac{1}{4}$	b $) n π \pm π / 4$
$3) {sin}^{2} θ = \frac{1}{4}$	c $) n π \pm π / 3$
4) cosec $θ = 1$	d) $n π \pm π / 2$ $e) n π \pm π / 8$

Which of the following statements are correct?

1 . if sin θ = sin α ⇒ θ = nπ + $(- 1)^{n}$ α where α ∈ [ - $\frac{π}{2}$ , $\frac{π}{2}$ ] n ∈ I

2 . if cos θ = cos α ⇒ 2nπ±α where α ∈ [0,π] n ∈ I

3 . if tan θ = tan α ⇒ θ = nπ + α where α ∈ (- $\frac{π}{2}$ , $\frac{π}{2}$ ) n ∈ I

Q. The general solution of

(\sqrt{3} - 1) sin θ + (\sqrt{3} + 1) cos θ = 2

is
(where

n \in Z

)

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If √3cos2θ−2√3sinθcosθ−3sin2θ=0, then

The correct option is B None of the above√3cos2θ−3√3sinθcosθ+sinθcosθ−3sin2θ=0√3cosθ(cosθ−3sinθ)+sinθ(cosθ−3sinθ)=0(cosθ−3sinθ)(√3cosθ+sinθ)=0tanθ=13Or, tanθ=−√3So, θ=nπ+tan−1(13)Or θ=nπ−π3

If $\sqrt{3} {cos}^{2} θ - 2 \sqrt{3} sin θ cos θ - 3 {sin}^{2} θ = 0$ , then