Q59 / 90 · JEE Main 2021 (26 Feb Shift 1) · Mathematics

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 ________.

Correct answer: 1

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

Hence, only one solution.

Hence, the correct answer is 1.