If θ ∈ [-2π, 2π], then the number of solutions of 2√2 cos^2 θ + (2-√6) cos θ - √3 = 0, is equal to:

Question

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:

(1) 12

(2) 6

(3) 8

(4) 10 

Answer 1

Correct option is: (3) 8    

\(2 \sqrt{2} \cos ^{2} \theta+2 \cos \theta-\sqrt{6} \cos \theta-\sqrt{3}=0\)

\((2 \cos \theta-\sqrt{3})(\sqrt{2} \cos \theta+1)=0\)

\(\cos \theta=\frac{\sqrt{3}}{2}, \frac{-1}{\sqrt{2}}\)

Number of solution = 8