JEE PYQ: Trigonometric Equations And Inequations Question 7
Question 7 - 2021 (26 Feb Shift 1)
If $\sqrt{3}(\cos^2 x) = (\sqrt{3} - 1) \cos x + 1$, the number of solutions of the given equation when $x \in \left[0, \frac{\pi}{2}\right]$ is:
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Answer: 1
Solution
$\sqrt{3}t^2 - (\sqrt{3}-1)t - 1 = 0$ (where $t = \cos x$)
$t = \cos x = 1$ or $-\frac{1}{\sqrt{3}}$ (rejected as $x \in [0, \frac{\pi}{2}]$)
No. of solutions $= 1$
BETA
