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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

For - (π)/(2) ≤ x ≤ (π)/(2), the number of points of intersection...

For −π2≤x≤π2,- \dfrac{\pi}{2} \le x \le \dfrac{\pi}{2}, the number of points of intersection of curves y=cosxy = cos x and y=sin⁡3xy = \sin 3x is

Options

  1. A00
  2. B11
  3. C22
  4. D33

Correct answer

D. 33

Step-by-step solution

y=cosx;y=sin⁡3xy = cos x; y = \sin 3x
⇒cosx=cos⁡(π2−3x)⇒x=2nπ±(π2−3x)⇒ cos x = \cos \left(\dfrac{\pi}{2} - 3x\right) ⇒ x = 2n\pi \pm \left(\dfrac{\pi}{2} - 3x\right)
⇒4x=2nπ+π2,−2x=2nπ−π2⇒ 4x = 2n\pi + \dfrac{\pi}{2}, - 2x = 2n\pi - \dfrac{\pi}{2}
⇒x=nπ2+π8,x=kπ+π4⇒ x = \dfrac{n\pi}{2} + \dfrac{\pi}{8}, x = k\pi + \dfrac{\pi}{4}
⇒x=(4n+1)π8,x=(4k+1)π4⇒ x = \left(4n + 1\right)\dfrac{\pi}{8}, x = \left(4k + 1\right)\dfrac{\pi}{4}
n=0⇒x=π8,n = 0 ⇒ x = \dfrac{\pi}{8}, k=0⇒x=π4k = 0 ⇒ x = \dfrac{\pi}{4}
n=−1⇒x=−3π8n = - 1 ⇒ x = \dfrac{- 3\pi}{8}
⇒x=−3π8,π8⇒ x = \dfrac{- 3\pi}{8}, \dfrac{\pi}{8} and π4\dfrac{\pi}{4}
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