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The number of values of $x \in [0, 4 π]$ satisfying $|\sqrt{3} \cos x - \sin x| \geq 2$ is

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Correct option is C

We have x∈0,4π and 3cosx-sinx≥2But 3cosx−sinx≤3+1=2Thus we must have 3cosx−sinx=2 ⇒32cosx−12sinx=1 ⇒cosx+π6=1 ⇒cosx+π6=1,−1⇒ x+π6=0,2π,4π,6π.....π,3π,5π,.... ∴x=11π6,23π6 ,5π6,17π6 ∵x∈0,4π

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The number of values of x∈0,4π satisfying 3cosx−sinx≥2is

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The number of values of $x \in [0, 4 π]$ satisfying $|\sqrt{3} \cos x - \sin x| \geq 2$ is