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

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of values of x ∈ [-2π,2π] which satisfy the equation...

The number of values of x∈x \in\left[-2\pi,2\pi\right]whichsatisfytheequationwhich satisfy the equationcosecx = 1 + cot x is equal to

Options

  1. A00
  2. B22
  3. C44
  4. D66

Correct answer

B. 22

Step-by-step solution

cosecx=1+cotxcosecx = 1 + cot x
1sinx=sinx+cosxsinx\dfrac{1}{sin x} = \dfrac{sin x + cos x}{sin x}
⇒sinx+cosx=1⇒ sin x + cos x = 1 and sinx≠0sin x \ne 0
⇒cos⁡(x−π4)=12⇒ \cos \left(x - \dfrac{\pi}{4}\right) = \dfrac{1}{\sqrt{2}}
⇒x−π4=±π4,±7π4⇒ x - \dfrac{\pi}{4} = \pm \dfrac{\pi}{4}, \pm \dfrac{7\pi}{4}
⇒x=0,π2,2π,−3π2⇒ x = 0, \dfrac{\pi}{2}, 2\pi, - \dfrac{3\pi}{2}
But, sinx≠0⇒x=π2,−3π2sin x \ne 0 ⇒ x = \dfrac{\pi}{2}, - \dfrac{3\pi}{2}
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