If 5 cos 2 - - 2 cos-2 -2 - -1- when -0 lt- - lt- - then the values of - are-

The correct option is D Given equation is 5 cos 2 θ + 2 cos^2 θ/2 + 1 = 0 ⇒ 5(2 cos^2 θ 1) + 1 + cosθ + 1 = 0 ⇒ 10 cos^2 θ + cosθ 3 = 0 ⇒ (2 cosθ 1)(5cosθ+ ...

Byju's Answer

Standard XI

Mathematics

Principal Solution of Trigonometric Equation

If 5 cos 2 θ ...

Question

If $5 cos 2 θ + 2 {cos}^{2} \frac{θ}{2} = - 1,$ when $(0 < θ < π),$ then the values of $θ$ are

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Solution

The correct option is D
Given equation is
$5 cos 2 θ + 2 {cos}^{2} \frac{θ}{2} + 1 = 0$
$\Rightarrow 5 (2 {cos}^{2} θ - 1) + 1 + cos θ + 1 = 0$
$\Rightarrow 10 {cos}^{2} θ + cos θ - 3 = 0$
$\Rightarrow (2 cos θ - 1) (5 cos θ + 3) = 0$
$\Rightarrow cos θ = \frac{1}{2}$ or $cos θ = - \frac{3}{5}$
$\Rightarrow θ = \frac{π}{3}$ or $θ = π - {cos}^{- 1} (\frac{3}{5})$

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If 5cos2θ+2cos2θ2=−1, when (0<θ<π), then the values of θ are

The correct option is D Given equation is 5cos2θ+2cos2θ2+1=0 ⇒5(2cos2θ−1)+1+cosθ+1=0 ⇒10cos2θ+cosθ−3=0 ⇒(2cosθ−1)(5cosθ+3)=0 ⇒cosθ=12 or cosθ=−35 ⇒θ=π3 or θ=π−cos−1(35)

If $5 cos 2 θ + 2 {cos}^{2} \frac{θ}{2} = - 1,$ when $(0 < θ < π),$ then the values of $θ$ are