X - R- cos 2 x-2 cos 2 x-2 is equal toA- 2 n -3- n - Z- 2 n -3- n - Z- n -J-6- n - ZD- n -3- n - Z

The correct option is C Given equation is cos 2x + 2 cos^2 x = 2 ⇒ 2 cos^2 x – 1 + 2 cos^2 x = 2 ⇒ 4 cos^2 x = 3 ⇒cos^2 x = 3/4 ⇒cos^2 x = cos^2 π/6 ⇒ x = n ...

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Standard XI

Mathematics

General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

x ∈ R: cos 2 ...

Question

${x \in R : cos 2 x + 2 {cos}^{2} x = 2}$ is equal to

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Solution

The correct option is B
Given equation is $cos 2 x + 2 {cos}^{2} x = 2$
$\Rightarrow 2 {cos}^{2} x - 1 + 2 {cos}^{2} x = 2$
$\Rightarrow 4 {cos}^{2} x = 3$
$\Rightarrow {cos}^{2} x = \frac{3}{4}$
$\Rightarrow {cos}^{2} x = {cos}^{2} \frac{π}{6}$
$\Rightarrow x = n π \pm \frac{π}{6} : n \in Z$

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{x∈R:cos2x+2cos2x=2} is equal to

The correct option is B Given equation is cos2x+2cos2x=2 ⇒2cos2x–1+2cos2x=2 ⇒4cos2x=3 ⇒cos2x=34 ⇒cos2x=cos2π6 ⇒x=nπ±π6:n∈Z

${x \in R : cos 2 x + 2 {cos}^{2} x = 2}$ is equal to

The correct option is B
Given equation is $cos 2 x + 2 {cos}^{2} x = 2$
$\Rightarrow 2 {cos}^{2} x - 1 + 2 {cos}^{2} x = 2$
$\Rightarrow 4 {cos}^{2} x = 3$
$\Rightarrow {cos}^{2} x = \frac{3}{4}$
$\Rightarrow {cos}^{2} x = {cos}^{2} \frac{π}{6}$
$\Rightarrow x = n π \pm \frac{π}{6} : n \in Z$