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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · medium

The expression (1-cos 2θ)/(sin 2θ) is equal to

Single correct option

The expression 1−cos⁡2θsin⁡2θ\dfrac{1-\cos2\theta}{\sin2\theta} is equal to
  1. A. cot⁡θ\cot\theta
  2. B. tan⁡θ\tan\theta
  3. C. sin⁡θ\sin\theta
  4. D. sec⁡θ\sec\theta
Show answer and solution

Answer: (B) tan⁡θ\tan\theta

Use 1−cos⁡2θ=2sin⁡2θ1-\cos2\theta=2\sin^2\theta and sin⁡2θ=2sin⁡θcos⁡θ\sin2\theta=2\sin\theta\cos\theta. The ratio is 2sin⁡2θ2sin⁡θcos⁡θ=tan⁡θ\dfrac{2\sin^2\theta}{2\sin\theta\cos\theta}=\tan\theta. The cot⁡θ\cot\theta option results from using 1+cos⁡2θ1+\cos2\theta in the numerator.
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Original question written in the NDA 2016 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