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Number of solutions of the equation $4 (\cos^{2} 2 x + \cos 2 x + 1)$ $+ \tan x (\tan x - 2 \sqrt{3}) = 0 in [0, 2 π]$ is

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Correct option is C

4cos2⁡2x+4cos⁡2x+1+tan2⁡x−23tan⁡x+3=0⇒ (2cos⁡2x+1)2+(tan⁡x−3)2=0⇒ cos⁡2x=−12 and tan⁡x=3⇒ 2cos2⁡x−1=−12 and tan⁡x=3⇒ cos⁡x=±12 and tan⁡x=3⇒ x=π3,4π3Thus, number of solutions of equation is 2.

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Number of solutions of the equation 4cos2⁡2x+cos⁡2x+1 +tan⁡x(tan⁡x−23)=0 in [0,2π] is

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Number of solutions of the equation $4 (\cos^{2} 2 x + \cos 2 x + 1)$ $+ \tan x (\tan x - 2 \sqrt{3}) = 0 in [0, 2 π]$ is