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JEE Main 202229 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2022 · 29 June · Evening Shift · Mathematics · Trigonometric Equations

The number of solutions of the equation x = ^ 2 x in the interval...

The number of solutions of the equation sin⁡x=cos⁡2x\sin x = \cos^{2}x in the interval (0,10)\left(0, 10\right) is ______.The number of solutions of the equation x = ^ 2 x in the interval (0, 10) is ______.

Correct answer

0

Step-by-step solution

Given, sin⁡x=cos⁡2x\sin x = \cos^{2}x

⇒sin⁡x=1−sin⁡2x⇒ \sin x = 1 - \sin^{2}x

⇒sin⁡2x+sin⁡x−1=0⇒ \sin^{2}x + \sin x - 1 = 0

⇒sin⁡x=(−1±5)2⇒ \sin x = \dfrac{\left(- 1 \pm \sqrt{5}\right)}{2}

⇒sin⁡x=(5−1)2⇒ \sin x = \dfrac{\left(\sqrt{5} - 1\right)}{2}

Now plotting the graph we get,

The number of solutions of the equation x = ^ 2 x in the interval (0, 10) is ______.

⇒⇒Now by graph number of solutions in \left(0, 10\right) = 4$

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