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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Trigonometric Equations

BITSAT 2023 · Paper 1 · Mathematics · Trigonometric Equations

If ^2 θ=(4)/(3) , then the general value of θ is

If sec⁡2θ=43\sec ^2 \theta=\frac{4}{3}, then the general value of θ\theta is

Options

  1. A2nπ±π62 \mathrm{n} \pi \pm \frac{\pi}{6}
  2. Bnπ±π6\mathrm{n} \pi \pm \frac{\pi}{6}
  3. C2nπ±π32 \mathrm{n} \pi \pm \frac{\pi}{3}
  4. Dnπ±π3\mathrm{n} \pi \pm \frac{\pi}{3}

Correct answer

B. nπ±π6\mathrm{n} \pi \pm \frac{\pi}{6}

Step-by-step solution

We have sec⁡2θ=43⇒cos⁡2θ=34\sec ^2 \theta=\frac{4}{3} \Rightarrow \cos ^2 \theta=\frac{3}{4}
⇒cos⁡2θ=cos⁡2(π6)⇒\Rightarrow \cos ^2 \theta=\cos ^2\left(\frac{\pi}{6}\right) \Rightarrow
θ=nπ±π6………\theta=n \pi \pm \frac{\pi}{6} \ldots \ldots \ldots
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