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

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The solution of the equation ^ 2 x + ^ 2 3x = 1 is&

The solution of the equation sin⁡2x+cos⁡23x=1\sin^{2} x + \cos^{2} 3x = 1 is&

Options

  1. Ax=nπ3x = \dfrac{n\pi}{3}
  2. Bx=nπ+π4x = n\pi + \dfrac{\pi}{4}
  3. Cx=nπ4x = \dfrac{n\pi}{4}
  4. Dx=nπ+π2x = n\pi + \dfrac{\pi}{2}

Correct answer

C. x=nπ4x = \dfrac{n\pi}{4}

Step-by-step solution

sin⁡2x=1−cos⁡23x=sin⁡23x\sin^{2} x = 1 - \cos^{2} 3x = \sin^{2} 3x
sin⁡23x−sin⁡2x=0\sin^{2} 3x - \sin^{2} x = 0
sin⁡4xsin2x=0\sin 4xsin 2x = 0
sin⁡2x=0⇒2x=nπ⇒x=nπ2\sin 2x = 0 ⇒ 2x = n\pi ⇒ x = \dfrac{n\pi}{2}
or
sin⁡4x=0⇒4x=nπ⇒x=nπ4\sin 4x = 0 ⇒ 4x = n\pi ⇒ x = \dfrac{n\pi}{4}
⇒x=nπ4⇒ x = \dfrac{n\pi}{4}
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