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  4. If √3( cos 2 x)=(√3-1) cos x+1, the number of solutions of the given equation when x ∈[0, (π/2)] is

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Q. If $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ the number of solutions of the given equation when $x \in\left[0, \frac{\pi}{2}\right]$ is

JEE MainJEE Main 2021Probability - Part 2

Solution:

$\sqrt{3}(\cos x)^{2}-\sqrt{3} \cos x+\cos x-1=0$
$\Rightarrow (\sqrt{3} \cos x+1)(\cos x-1)=0$
$\Rightarrow \cos x=1$ or $\cos x=-\frac{1}{\sqrt{3}}$ (reject)
$\Rightarrow x=0$ only