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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 ordered pairs (a, x) satisfying the equation ^ 2 (a +...

The number of ordered pairs (a,x)\left(a, x\right) satisfying the equation sec⁡2(a+2)x+a2−1=0,−π<x<π\sec^{2} \left(a + 2\right)x + a^{2} - 1 = 0, - \pi < x < \pi is

Options

  1. A11
  2. B22
  3. C33
  4. D44

Correct answer

C. 33

Step-by-step solution

Given equation is sec⁡2(a+2)x+a2−1=0\sec^{2} \left(a + 2\right)x + a^{2} - 1 = 0
⇒tan⁡2(a+2)x+a2=0⇒ \tan^{2} \left(a + 2\right)x + a^{2} = 0
⇒tan⁡(a+2)x=0⇒ \tan \left(a + 2\right)x = 0 and a=0a = 0
⇒tan⁡2x=0⇒ \tan 2x = 0
⇒x=0,π2,−π2.⇒ x = 0, \dfrac{\pi}{2}, - \dfrac{\pi}{2}.
So, \left(0, 0\right), \left(0, \dfrac{\pi}{2}\right),(0,−π2), \left(0, - \dfrac{\pi}{2}\right)are ordered pairs (a,x)\left(a, x\right) satisfying the equation.
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