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JEE Main 202126 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
26 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2021 · 26 February · Morning Shift · Mathematics · Trigonometric Equations

If 3 ( ^ 2 x) = ( 3 - 1) x + 1 , then number of solutions of the...

If 3(cos⁡2x)=(3−1)cos⁡x+1\sqrt{3}\left(\cos^{2}x\right) = \left(\sqrt{3} - 1\right)\cos x + 1, then number of solutions of the given equation when x∈[0,π2]x \in \left[0, \dfrac{\pi}{2}\right] is ________.

Correct answer

0

Step-by-step solution

3(cos⁡x)2−3cos⁡x+cos⁡x−1=0\sqrt{3}{\left(\cos x\right)}^{2} - \sqrt{3}\cos x + \cos x - 1 = 0

⇒(3cos⁡x+1)(cos⁡x−1)=0⇒ \left(\sqrt{3}\cos x + 1\right)\left(\cos x - 1\right) = 0

⇒cos⁡x=1⇒ \cos x = 1 or cos⁡x=−13\cos x = - \dfrac{1}{\sqrt{3}} (reject)

⇒x=0⇒ x = 0 only

Hence, only one solution.

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