If θ ∈[-2 π, 2 π] , then number of solutions of 2 √{2} cos ^2 θ+(2-√{6}) cos θ-√{3}=0 ,

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Trigonometrical Equations

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If $\theta \in[-2 \pi, 2 \pi]$, then the number of solutions of $2 \sqrt{2} \cos ^2 \theta+(2-\sqrt{6}) \cos \theta-\sqrt{3}=0$, is equal to:

A$12$

B$6$

C$8$

D$10$

(JEE MAIN-2025)

Solution

$2 \sqrt{2} \cos ^2 \theta+2 \cos \theta-\sqrt{6} \cos \theta-\sqrt{3}=0$
$(2 \cos \theta-\sqrt{3})(\sqrt{2} \cos \theta+1)=0$
$\cos \theta=\frac{\sqrt{3}}{2}, \frac{-1}{\sqrt{2}}$
Number of solution $=8$

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