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NDA 2021 Maths · Mathematics · Trigonometric Equations · hard

The smallest positive value of θ for which cos θ=-1/2 and tan θ=√3 hold together is

Single correct option

The smallest positive value of θ\theta for which cos⁡θ=−12\cos\theta=-\dfrac12 and tan⁡θ=3\tan\theta=\sqrt3 hold together is
  1. A. 2π3\dfrac{2\pi}3
  2. B. π3\dfrac\pi3
  3. C. 4π3\dfrac{4\pi}3
  4. D. 5π6\dfrac{5\pi}6
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Answer: (C) 4π3\dfrac{4\pi}3

cos⁡θ=−12\cos\theta=-\tfrac12 gives 2π3\tfrac{2\pi}3 or 4π3\tfrac{4\pi}3; tan⁡θ=3\tan\theta=\sqrt3 gives π3\tfrac\pi3 or 4π3\tfrac{4\pi}3. The common value is 4π3\tfrac{4\pi}3, in the third quadrant where both cosine is negative and tangent positive.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake