The solution set of 5-4 cos - 2 cos -1-0 in the interval -0-2- is

The correct option is D 2π/3,4π/3 (5+4cos θ) (2cos θ+1)=0 ⇒cos θ= 5/4 (not possible) cos θ= 1/2 ⇒cosθ= 1/2 ⇒cosθ= cosπ3=cos(π±π3 ...

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Standard XII

Mathematics

Angle between Two Vectors

The solution ...

Question

The solution set of $(5 + 4 c o s θ) (2 c o s θ + 1) = 0$ in the interval $[0, 2 π]$ is

{\begin{matrix} \frac{π}{3}, \frac{2 π}{3} \end{matrix}}

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{\begin{matrix} \frac{π}{3}, π \end{matrix}}

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{\begin{matrix} \frac{2 π}{3}, \frac{4 π}{3} \end{matrix}}

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{\begin{matrix} \frac{2 π}{3}, \frac{5 π}{3} \end{matrix}}

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Solution

The correct option is D ${\begin{matrix} \frac{2 π}{3}, \frac{4 π}{3} \end{matrix}}$
$(5 + 4 cos θ) (2 cos θ + 1) = 0$
$\Rightarrow cos θ = - \frac{5}{4}$ (not possible) $cos θ = - \frac{1}{2}$
$\Rightarrow cos θ = - \frac{1}{2}$
$\Rightarrow cos θ = - cos \frac{π}{3} = cos (π \pm \frac{π}{3})$
$\Rightarrow θ = \frac{2 π}{3}, \frac{4 π}{3}$ (II and III quad, cosine is negaitve)

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