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NDA 2020 Maths · Mathematics · Trigonometric Functions and Identities · medium

If tan θ+cot θ=5, then sin 2θ equals

Single correct option

If tan⁡θ+cot⁡θ=5\tan\theta+\cot\theta=5, then sin⁡2θ\sin2\theta equals
  1. A. 25\dfrac25
  2. B. 15\dfrac15
  3. C. 45\dfrac45
  4. D. 25\dfrac{2}{\sqrt5}
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Answer: (A) 25\dfrac25

tan⁡θ+cot⁡θ=sin⁡2θ+cos⁡2θsin⁡θcos⁡θ=2sin⁡2θ\tan\theta+\cot\theta=\dfrac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}=\dfrac{2}{\sin2\theta}. So 2sin⁡2θ=5\dfrac2{\sin2\theta}=5 and sin⁡2θ=25\sin2\theta=\dfrac25. The value 1/51/5 is sin⁡θcos⁡θ\sin\theta\cos\theta.
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Original question written in the NDA 2020 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