If 3 cos 2 x = 3 - 1 cos x + 1 , then number of solutions of the given equation when x ∈ 0 , π 2 is ________.

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Question: Answered & Verified by Expert

If

\sqrt{3} (\cos^{2} x) = (\sqrt{3} - 1) \cos x + 1

, then number of solutions of the given equation when

x \in [0, \frac{π}{2}]

is ________.

MathematicsTrigonometric EquationsJEE MainJEE Main 2021 (26 Feb Shift 1)

Solution:

1765 Upvotes Verified Answer

The correct answer is: 1

\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

Hence, only one solution.

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