PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · medium

If tan θ+cot θ=4, then sin 2θ equals

Single correct option

If tan⁡θ+cot⁡θ=4\tan\theta+\cot\theta=4, then sin⁡2θ\sin2\theta equals
  1. A. 12\dfrac12
  2. B. 14\dfrac14
  3. C. 22
  4. D. 32\dfrac{\sqrt3}2
Show answer and solution

Answer: (A) 12\dfrac12

We have tan⁡θ+cot⁡θ=sin⁡2θ+cos⁡2θsin⁡θcos⁡θ=1sin⁡θcos⁡θ=2sin⁡2θ\tan\theta+\cot\theta=\dfrac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}=\dfrac{1}{\sin\theta\cos\theta}=\dfrac{2}{\sin2\theta}. Setting this equal to 44 gives sin⁡2θ=12\sin2\theta=\dfrac12. The value 14\dfrac14 is sin⁡θcos⁡θ\sin\theta\cos\theta, and 22 is impossible since sin⁡2θ≤1\sin2\theta\le1, which gives a quick elimination.
Report a mistake

Original question written in the NDA 2019 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